Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

Question

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Answer 1

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 12, Problem 50DE

a.

To determine

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

a.

Expert Solution

Answer to Problem 50DE

There is no difference in the variance in team salary among the people from Country A and National league teams.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the variance in team salary among Country A and National league teams.

Alternative hypothesis: There is difference in the variance in team salary among Country A and National league teams.

Step-by-step procedure to obtain the test statistic using Excel:

In the first column, enter the salaries of Country A’s team.
In the second column, enter the salaries of National team.
Select the Data tab on the top menu.
Select Data Analysis and Click on: F-Test, Two-sample for variances and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 1

From the above output, the F- test statistic value is 2.37 and its p-value is 0.056.

Decision Rule:

If the p-value is less than the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Conclusion:

The significance level is 0.05. The p-value is 0.056 and it is greater than the significance level. The null hypothesis is rejected at the 0.05 significance level.

Thus, there is no difference in the variance in team salary among Country A and National league teams.

b.

To determine

Create a variable that classifies a team’s total attendance into three groups.

Find whether there is a difference in the mean number of games won among the three groups.

b.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of games won among the three groups.

Explanation of Solution

Let X represent the total attendance into three groups. Samples 1, 2, and 3 are “less than 2 (million)”, 2 up to 3, and 3 or more attendance of teams of three groups, respectively.

The following table gives the number of games won by the three groups of attendances.

Sample 1	Sample 2	Sample 3
85	81	69
68	94	88
55	93	89
72	61	86
94	97	74
75	64	81
	69	94
	83	88
	66	93
	95
	79
	76
	73
	98

The null and alternative hypotheses are as follows:

Null hypothesis: There is no difference in the mean number of games won among the three groups.

Alternative hypothesis: There is a difference in the mean number of games won among the three groups

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of games won by the team, which is less than 2 million attendances.
In Sample 2, enter the number of games won by the team of 2 up to 3 million attendances.
In Sample 3, enter the number of games won by the team of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 2

From the above output, the F test statistic value is 1.22 and the p-value is 0.31.

Conclusion:

The level of significance is 0.05. The p-value is greater than the significance level. Hence, one can fail to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of games won among the three groups.

c.

To determine

Find whether there is a difference in the mean number of home runs hit per team using the variable defined in Part b.

c.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of home runs hit per team.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the mean number of home runs hit per team.

Alternative hypothesis: There is a difference in the mean number of home runs hit per team.

The following table gives the number of home runs per each team, which is defined in Part b.

Sample 1	Sample 2	Sample 3
211	165	165
136	149	163
146	214	187
131	137	116
195	172	245
149	166	158
175	137	103
	202	159
	131	200
	139
	170
	121
	198
	194

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of home runs hit by the group of less than 2 million attendances.
In Sample 2, enter the number of home runs hit by the group of 2 up to 3 million attendances.
In Sample 3, enter the number of home runs hit by the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 3

From the above output, the F test statistic value is 0.018 and the p-value is 0.9823.

Conclusion:

The level of significance is 0.05 and the p-value is greater than the significance level. Hence, one fails to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of home runs hit per team.

d.

To determine

Find whether there is a difference in the mean salary of the three groups.

d.

Expert Solution

Answer to Problem 50DE

The mean salaries are different for each group.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: The mean salary of the three groups is equal.

Alternative hypothesis: At least one mean salary is different from other.

The following table provides the salary of each group that is defined in Part b.

Sample 1	Sample 2	Sample 3
96.9	74.3	173.2
78.4	83.3	132.3
60.7	81.4	154.5
60.9	88.2	95.1
55.4	82.2	198
82	78.1	174.5
64.2	118.1	117.6
	97.7	110.3
	94.1	120.5
	93.4
	63.4
	55.2
	75.5
	81.3

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the salary of the group of less than 2 million attendances.
In Sample 2, enter the salary of the group of 2 up to 3 million attendances.
In Sample 3, enter the salary of the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 4

From the above output, the F test statistic value is 24.31 and the p-value is 0.

Conclusion:

The level of significance is 0.05 and the p-value is less than the significance level. Hence, one can reject the null hypothesis at the 0.05 significance level. Thus, the mean salaries are different for each group.

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Answer 2

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 12, Problem 50DE

a.

To determine

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

a.

Expert Solution

Answer to Problem 50DE

There is no difference in the variance in team salary among the people from Country A and National league teams.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the variance in team salary among Country A and National league teams.

Alternative hypothesis: There is difference in the variance in team salary among Country A and National league teams.

Step-by-step procedure to obtain the test statistic using Excel:

In the first column, enter the salaries of Country A’s team.
In the second column, enter the salaries of National team.
Select the Data tab on the top menu.
Select Data Analysis and Click on: F-Test, Two-sample for variances and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 1

From the above output, the F- test statistic value is 2.37 and its p-value is 0.056.

Decision Rule:

If the p-value is less than the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Conclusion:

The significance level is 0.05. The p-value is 0.056 and it is greater than the significance level. The null hypothesis is rejected at the 0.05 significance level.

Thus, there is no difference in the variance in team salary among Country A and National league teams.

b.

To determine

Create a variable that classifies a team’s total attendance into three groups.

Find whether there is a difference in the mean number of games won among the three groups.

b.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of games won among the three groups.

Explanation of Solution

Let X represent the total attendance into three groups. Samples 1, 2, and 3 are “less than 2 (million)”, 2 up to 3, and 3 or more attendance of teams of three groups, respectively.

The following table gives the number of games won by the three groups of attendances.

Sample 1	Sample 2	Sample 3
85	81	69
68	94	88
55	93	89
72	61	86
94	97	74
75	64	81
	69	94
	83	88
	66	93
	95
	79
	76
	73
	98

The null and alternative hypotheses are as follows:

Null hypothesis: There is no difference in the mean number of games won among the three groups.

Alternative hypothesis: There is a difference in the mean number of games won among the three groups

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of games won by the team, which is less than 2 million attendances.
In Sample 2, enter the number of games won by the team of 2 up to 3 million attendances.
In Sample 3, enter the number of games won by the team of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 2

From the above output, the F test statistic value is 1.22 and the p-value is 0.31.

Conclusion:

The level of significance is 0.05. The p-value is greater than the significance level. Hence, one can fail to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of games won among the three groups.

c.

To determine

Find whether there is a difference in the mean number of home runs hit per team using the variable defined in Part b.

c.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of home runs hit per team.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the mean number of home runs hit per team.

Alternative hypothesis: There is a difference in the mean number of home runs hit per team.

The following table gives the number of home runs per each team, which is defined in Part b.

Sample 1	Sample 2	Sample 3
211	165	165
136	149	163
146	214	187
131	137	116
195	172	245
149	166	158
175	137	103
	202	159
	131	200
	139
	170
	121
	198
	194

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of home runs hit by the group of less than 2 million attendances.
In Sample 2, enter the number of home runs hit by the group of 2 up to 3 million attendances.
In Sample 3, enter the number of home runs hit by the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 3

From the above output, the F test statistic value is 0.018 and the p-value is 0.9823.

Conclusion:

The level of significance is 0.05 and the p-value is greater than the significance level. Hence, one fails to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of home runs hit per team.

d.

To determine

Find whether there is a difference in the mean salary of the three groups.

d.

Expert Solution

Answer to Problem 50DE

The mean salaries are different for each group.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: The mean salary of the three groups is equal.

Alternative hypothesis: At least one mean salary is different from other.

The following table provides the salary of each group that is defined in Part b.

Sample 1	Sample 2	Sample 3
96.9	74.3	173.2
78.4	83.3	132.3
60.7	81.4	154.5
60.9	88.2	95.1
55.4	82.2	198
82	78.1	174.5
64.2	118.1	117.6
	97.7	110.3
	94.1	120.5
	93.4
	63.4
	55.2
	75.5
	81.3

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the salary of the group of less than 2 million attendances.
In Sample 2, enter the salary of the group of 2 up to 3 million attendances.
In Sample 3, enter the salary of the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 4

From the above output, the F test statistic value is 24.31 and the p-value is 0.

Conclusion:

The level of significance is 0.05 and the p-value is less than the significance level. Hence, one can reject the null hypothesis at the 0.05 significance level. Thus, the mean salaries are different for each group.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 12, Problem 50DE

a.

To determine

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

a.

Expert Solution

Answer to Problem 50DE

There is no difference in the variance in team salary among the people from Country A and National league teams.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the variance in team salary among Country A and National league teams.

Alternative hypothesis: There is difference in the variance in team salary among Country A and National league teams.

Step-by-step procedure to obtain the test statistic using Excel:

In the first column, enter the salaries of Country A’s team.
In the second column, enter the salaries of National team.
Select the Data tab on the top menu.
Select Data Analysis and Click on: F-Test, Two-sample for variances and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 1

From the above output, the F- test statistic value is 2.37 and its p-value is 0.056.

Decision Rule:

If the p-value is less than the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Conclusion:

The significance level is 0.05. The p-value is 0.056 and it is greater than the significance level. The null hypothesis is rejected at the 0.05 significance level.

Thus, there is no difference in the variance in team salary among Country A and National league teams.

b.

To determine

Create a variable that classifies a team’s total attendance into three groups.

Find whether there is a difference in the mean number of games won among the three groups.

b.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of games won among the three groups.

Explanation of Solution

Let X represent the total attendance into three groups. Samples 1, 2, and 3 are “less than 2 (million)”, 2 up to 3, and 3 or more attendance of teams of three groups, respectively.

The following table gives the number of games won by the three groups of attendances.

Sample 1	Sample 2	Sample 3
85	81	69
68	94	88
55	93	89
72	61	86
94	97	74
75	64	81
	69	94
	83	88
	66	93
	95
	79
	76
	73
	98

The null and alternative hypotheses are as follows:

Null hypothesis: There is no difference in the mean number of games won among the three groups.

Alternative hypothesis: There is a difference in the mean number of games won among the three groups

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of games won by the team, which is less than 2 million attendances.
In Sample 2, enter the number of games won by the team of 2 up to 3 million attendances.
In Sample 3, enter the number of games won by the team of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 2

From the above output, the F test statistic value is 1.22 and the p-value is 0.31.

Conclusion:

The level of significance is 0.05. The p-value is greater than the significance level. Hence, one can fail to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of games won among the three groups.

c.

To determine

Find whether there is a difference in the mean number of home runs hit per team using the variable defined in Part b.

c.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of home runs hit per team.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the mean number of home runs hit per team.

Alternative hypothesis: There is a difference in the mean number of home runs hit per team.

The following table gives the number of home runs per each team, which is defined in Part b.

Sample 1	Sample 2	Sample 3
211	165	165
136	149	163
146	214	187
131	137	116
195	172	245
149	166	158
175	137	103
	202	159
	131	200
	139
	170
	121
	198
	194

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of home runs hit by the group of less than 2 million attendances.
In Sample 2, enter the number of home runs hit by the group of 2 up to 3 million attendances.
In Sample 3, enter the number of home runs hit by the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 3

From the above output, the F test statistic value is 0.018 and the p-value is 0.9823.

Conclusion:

The level of significance is 0.05 and the p-value is greater than the significance level. Hence, one fails to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of home runs hit per team.

d.

To determine

Find whether there is a difference in the mean salary of the three groups.

d.

Expert Solution

Answer to Problem 50DE

The mean salaries are different for each group.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: The mean salary of the three groups is equal.

Alternative hypothesis: At least one mean salary is different from other.

The following table provides the salary of each group that is defined in Part b.

Sample 1	Sample 2	Sample 3
96.9	74.3	173.2
78.4	83.3	132.3
60.7	81.4	154.5
60.9	88.2	95.1
55.4	82.2	198
82	78.1	174.5
64.2	118.1	117.6
	97.7	110.3
	94.1	120.5
	93.4
	63.4
	55.2
	75.5
	81.3

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the salary of the group of less than 2 million attendances.
In Sample 2, enter the salary of the group of 2 up to 3 million attendances.
In Sample 3, enter the salary of the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 4

From the above output, the F test statistic value is 24.31 and the p-value is 0.

Conclusion:

The level of significance is 0.05 and the p-value is less than the significance level. Hence, one can reject the null hypothesis at the 0.05 significance level. Thus, the mean salaries are different for each group.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 12, Problem 50DE

a.

To determine

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

a.

Expert Solution

Answer to Problem 50DE

There is no difference in the variance in team salary among the people from Country A and National league teams.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the variance in team salary among Country A and National league teams.

Alternative hypothesis: There is difference in the variance in team salary among Country A and National league teams.

Step-by-step procedure to obtain the test statistic using Excel:

In the first column, enter the salaries of Country A’s team.
In the second column, enter the salaries of National team.
Select the Data tab on the top menu.
Select Data Analysis and Click on: F-Test, Two-sample for variances and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 1

From the above output, the F- test statistic value is 2.37 and its p-value is 0.056.

Decision Rule:

If the p-value is less than the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Conclusion:

The significance level is 0.05. The p-value is 0.056 and it is greater than the significance level. The null hypothesis is rejected at the 0.05 significance level.

Thus, there is no difference in the variance in team salary among Country A and National league teams.

b.

To determine

Create a variable that classifies a team’s total attendance into three groups.

Find whether there is a difference in the mean number of games won among the three groups.

b.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of games won among the three groups.

Explanation of Solution

Let X represent the total attendance into three groups. Samples 1, 2, and 3 are “less than 2 (million)”, 2 up to 3, and 3 or more attendance of teams of three groups, respectively.

The following table gives the number of games won by the three groups of attendances.

Sample 1	Sample 2	Sample 3
85	81	69
68	94	88
55	93	89
72	61	86
94	97	74
75	64	81
	69	94
	83	88
	66	93
	95
	79
	76
	73
	98

The null and alternative hypotheses are as follows:

Null hypothesis: There is no difference in the mean number of games won among the three groups.

Alternative hypothesis: There is a difference in the mean number of games won among the three groups

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of games won by the team, which is less than 2 million attendances.
In Sample 2, enter the number of games won by the team of 2 up to 3 million attendances.
In Sample 3, enter the number of games won by the team of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 2

From the above output, the F test statistic value is 1.22 and the p-value is 0.31.

Conclusion:

The level of significance is 0.05. The p-value is greater than the significance level. Hence, one can fail to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of games won among the three groups.

c.

To determine

Find whether there is a difference in the mean number of home runs hit per team using the variable defined in Part b.

c.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of home runs hit per team.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the mean number of home runs hit per team.

Alternative hypothesis: There is a difference in the mean number of home runs hit per team.

The following table gives the number of home runs per each team, which is defined in Part b.

Sample 1	Sample 2	Sample 3
211	165	165
136	149	163
146	214	187
131	137	116
195	172	245
149	166	158
175	137	103
	202	159
	131	200
	139
	170
	121
	198
	194

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of home runs hit by the group of less than 2 million attendances.
In Sample 2, enter the number of home runs hit by the group of 2 up to 3 million attendances.
In Sample 3, enter the number of home runs hit by the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 3

From the above output, the F test statistic value is 0.018 and the p-value is 0.9823.

Conclusion:

The level of significance is 0.05 and the p-value is greater than the significance level. Hence, one fails to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of home runs hit per team.

d.

To determine

Find whether there is a difference in the mean salary of the three groups.

d.

Expert Solution

Answer to Problem 50DE

The mean salaries are different for each group.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: The mean salary of the three groups is equal.

Alternative hypothesis: At least one mean salary is different from other.

The following table provides the salary of each group that is defined in Part b.

Sample 1	Sample 2	Sample 3
96.9	74.3	173.2
78.4	83.3	132.3
60.7	81.4	154.5
60.9	88.2	95.1
55.4	82.2	198
82	78.1	174.5
64.2	118.1	117.6
	97.7	110.3
	94.1	120.5
	93.4
	63.4
	55.2
	75.5
	81.3

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the salary of the group of less than 2 million attendances.
In Sample 2, enter the salary of the group of 2 up to 3 million attendances.
In Sample 3, enter the salary of the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 4

From the above output, the F test statistic value is 24.31 and the p-value is 0.

Conclusion:

The level of significance is 0.05 and the p-value is less than the significance level. Hence, one can reject the null hypothesis at the 0.05 significance level. Thus, the mean salaries are different for each group.

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Answer 5

Chapter 12, Problem 50DE

a.

To determine

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

a.

Expert Solution

Answer to Problem 50DE

There is no difference in the variance in team salary among the people from Country A and National league teams.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the variance in team salary among Country A and National league teams.

Alternative hypothesis: There is difference in the variance in team salary among Country A and National league teams.

Step-by-step procedure to obtain the test statistic using Excel:

In the first column, enter the salaries of Country A’s team.
In the second column, enter the salaries of National team.
Select the Data tab on the top menu.
Select Data Analysis and Click on: F-Test, Two-sample for variances and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 1

From the above output, the F- test statistic value is 2.37 and its p-value is 0.056.

Decision Rule:

If the p-value is less than the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Conclusion:

The significance level is 0.05. The p-value is 0.056 and it is greater than the significance level. The null hypothesis is rejected at the 0.05 significance level.

Thus, there is no difference in the variance in team salary among Country A and National league teams.

b.

To determine

Create a variable that classifies a team’s total attendance into three groups.

Find whether there is a difference in the mean number of games won among the three groups.

b.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of games won among the three groups.

Explanation of Solution

Let X represent the total attendance into three groups. Samples 1, 2, and 3 are “less than 2 (million)”, 2 up to 3, and 3 or more attendance of teams of three groups, respectively.

The following table gives the number of games won by the three groups of attendances.

Sample 1	Sample 2	Sample 3
85	81	69
68	94	88
55	93	89
72	61	86
94	97	74
75	64	81
	69	94
	83	88
	66	93
	95
	79
	76
	73
	98

The null and alternative hypotheses are as follows:

Null hypothesis: There is no difference in the mean number of games won among the three groups.

Alternative hypothesis: There is a difference in the mean number of games won among the three groups

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of games won by the team, which is less than 2 million attendances.
In Sample 2, enter the number of games won by the team of 2 up to 3 million attendances.
In Sample 3, enter the number of games won by the team of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 2

From the above output, the F test statistic value is 1.22 and the p-value is 0.31.

Conclusion:

The level of significance is 0.05. The p-value is greater than the significance level. Hence, one can fail to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of games won among the three groups.

c.

To determine

Find whether there is a difference in the mean number of home runs hit per team using the variable defined in Part b.

c.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of home runs hit per team.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the mean number of home runs hit per team.

Alternative hypothesis: There is a difference in the mean number of home runs hit per team.

The following table gives the number of home runs per each team, which is defined in Part b.

Sample 1	Sample 2	Sample 3
211	165	165
136	149	163
146	214	187
131	137	116
195	172	245
149	166	158
175	137	103
	202	159
	131	200
	139
	170
	121
	198
	194

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of home runs hit by the group of less than 2 million attendances.
In Sample 2, enter the number of home runs hit by the group of 2 up to 3 million attendances.
In Sample 3, enter the number of home runs hit by the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 3

From the above output, the F test statistic value is 0.018 and the p-value is 0.9823.

Conclusion:

The level of significance is 0.05 and the p-value is greater than the significance level. Hence, one fails to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of home runs hit per team.

d.

To determine

Find whether there is a difference in the mean salary of the three groups.

d.

Expert Solution

Answer to Problem 50DE

The mean salaries are different for each group.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: The mean salary of the three groups is equal.

Alternative hypothesis: At least one mean salary is different from other.

The following table provides the salary of each group that is defined in Part b.

Sample 1	Sample 2	Sample 3
96.9	74.3	173.2
78.4	83.3	132.3
60.7	81.4	154.5
60.9	88.2	95.1
55.4	82.2	198
82	78.1	174.5
64.2	118.1	117.6
	97.7	110.3
	94.1	120.5
	93.4
	63.4
	55.2
	75.5
	81.3

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the salary of the group of less than 2 million attendances.
In Sample 2, enter the salary of the group of 2 up to 3 million attendances.
In Sample 3, enter the salary of the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 4

From the above output, the F test statistic value is 24.31 and the p-value is 0.

Conclusion:

The level of significance is 0.05 and the p-value is less than the significance level. Hence, one can reject the null hypothesis at the 0.05 significance level. Thus, the mean salaries are different for each group.

Answer 6

Chapter 12, Problem 50DE

a.

To determine

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

a.

Expert Solution

Answer to Problem 50DE

There is no difference in the variance in team salary among the people from Country A and National league teams.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the variance in team salary among Country A and National league teams.

Alternative hypothesis: There is difference in the variance in team salary among Country A and National league teams.

Step-by-step procedure to obtain the test statistic using Excel:

In the first column, enter the salaries of Country A’s team.
In the second column, enter the salaries of National team.
Select the Data tab on the top menu.
Select Data Analysis and Click on: F-Test, Two-sample for variances and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 1

From the above output, the F- test statistic value is 2.37 and its p-value is 0.056.

Decision Rule:

If the p-value is less than the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Conclusion:

The significance level is 0.05. The p-value is 0.056 and it is greater than the significance level. The null hypothesis is rejected at the 0.05 significance level.

Thus, there is no difference in the variance in team salary among Country A and National league teams.

Answer 7

Chapter 12, Problem 50DE

a.

To determine

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

Answer 8

a.

Expert Solution

Answer to Problem 50DE

There is no difference in the variance in team salary among the people from Country A and National league teams.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the variance in team salary among Country A and National league teams.

Alternative hypothesis: There is difference in the variance in team salary among Country A and National league teams.

Step-by-step procedure to obtain the test statistic using Excel:

In the first column, enter the salaries of Country A’s team.
In the second column, enter the salaries of National team.
Select the Data tab on the top menu.
Select Data Analysis and Click on: F-Test, Two-sample for variances and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 1

From the above output, the F- test statistic value is 2.37 and its p-value is 0.056.

Decision Rule:

If the p-value is less than the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Conclusion:

The significance level is 0.05. The p-value is 0.056 and it is greater than the significance level. The null hypothesis is rejected at the 0.05 significance level.

Thus, there is no difference in the variance in team salary among Country A and National league teams.

Answer 13

b.

To determine

Create a variable that classifies a team’s total attendance into three groups.

Find whether there is a difference in the mean number of games won among the three groups.

b.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of games won among the three groups.

Explanation of Solution

Let X represent the total attendance into three groups. Samples 1, 2, and 3 are “less than 2 (million)”, 2 up to 3, and 3 or more attendance of teams of three groups, respectively.

The following table gives the number of games won by the three groups of attendances.

Sample 1	Sample 2	Sample 3
85	81	69
68	94	88
55	93	89
72	61	86
94	97	74
75	64	81
	69	94
	83	88
	66	93
	95
	79
	76
	73
	98

The null and alternative hypotheses are as follows:

Null hypothesis: There is no difference in the mean number of games won among the three groups.

Alternative hypothesis: There is a difference in the mean number of games won among the three groups

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of games won by the team, which is less than 2 million attendances.
In Sample 2, enter the number of games won by the team of 2 up to 3 million attendances.
In Sample 3, enter the number of games won by the team of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 2

From the above output, the F test statistic value is 1.22 and the p-value is 0.31.

Conclusion:

The level of significance is 0.05. The p-value is greater than the significance level. Hence, one can fail to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of games won among the three groups.

Answer 14

b.

To determine

Create a variable that classifies a team’s total attendance into three groups.

Find whether there is a difference in the mean number of games won among the three groups.

Answer 15

b.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of games won among the three groups.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Let X represent the total attendance into three groups. Samples 1, 2, and 3 are “less than 2 (million)”, 2 up to 3, and 3 or more attendance of teams of three groups, respectively.

The following table gives the number of games won by the three groups of attendances.

Sample 1	Sample 2	Sample 3
85	81	69
68	94	88
55	93	89
72	61	86
94	97	74
75	64	81
	69	94
	83	88
	66	93
	95
	79
	76
	73
	98

The null and alternative hypotheses are as follows:

Null hypothesis: There is no difference in the mean number of games won among the three groups.

Alternative hypothesis: There is a difference in the mean number of games won among the three groups

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of games won by the team, which is less than 2 million attendances.
In Sample 2, enter the number of games won by the team of 2 up to 3 million attendances.
In Sample 3, enter the number of games won by the team of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 2

From the above output, the F test statistic value is 1.22 and the p-value is 0.31.

Conclusion:

The level of significance is 0.05. The p-value is greater than the significance level. Hence, one can fail to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of games won among the three groups.

Answer 20

c.

To determine

Find whether there is a difference in the mean number of home runs hit per team using the variable defined in Part b.

c.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of home runs hit per team.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the mean number of home runs hit per team.

Alternative hypothesis: There is a difference in the mean number of home runs hit per team.

The following table gives the number of home runs per each team, which is defined in Part b.

Sample 1	Sample 2	Sample 3
211	165	165
136	149	163
146	214	187
131	137	116
195	172	245
149	166	158
175	137	103
	202	159
	131	200
	139
	170
	121
	198
	194

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of home runs hit by the group of less than 2 million attendances.
In Sample 2, enter the number of home runs hit by the group of 2 up to 3 million attendances.
In Sample 3, enter the number of home runs hit by the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 3

From the above output, the F test statistic value is 0.018 and the p-value is 0.9823.

Conclusion:

The level of significance is 0.05 and the p-value is greater than the significance level. Hence, one fails to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of home runs hit per team.

Answer 21

c.

To determine

Find whether there is a difference in the mean number of home runs hit per team using the variable defined in Part b.

Answer 22

c.

Expert Solution

Answer to Problem 50DE

There is no difference in the mean number of home runs hit per team.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in the mean number of home runs hit per team.

Alternative hypothesis: There is a difference in the mean number of home runs hit per team.

The following table gives the number of home runs per each team, which is defined in Part b.

Sample 1	Sample 2	Sample 3
211	165	165
136	149	163
146	214	187
131	137	116
195	172	245
149	166	158
175	137	103
	202	159
	131	200
	139
	170
	121
	198
	194

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the number of home runs hit by the group of less than 2 million attendances.
In Sample 2, enter the number of home runs hit by the group of 2 up to 3 million attendances.
In Sample 3, enter the number of home runs hit by the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 3

From the above output, the F test statistic value is 0.018 and the p-value is 0.9823.

Conclusion:

The level of significance is 0.05 and the p-value is greater than the significance level. Hence, one fails to reject the null hypothesis at the 0.05 significance level. Thus, there is no difference in the mean number of home runs hit per team.

Answer 27

d.

To determine

Find whether there is a difference in the mean salary of the three groups.

d.

Expert Solution

Answer to Problem 50DE

The mean salaries are different for each group.

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: The mean salary of the three groups is equal.

Alternative hypothesis: At least one mean salary is different from other.

The following table provides the salary of each group that is defined in Part b.

Sample 1	Sample 2	Sample 3
96.9	74.3	173.2
78.4	83.3	132.3
60.7	81.4	154.5
60.9	88.2	95.1
55.4	82.2	198
82	78.1	174.5
64.2	118.1	117.6
	97.7	110.3
	94.1	120.5
	93.4
	63.4
	55.2
	75.5
	81.3

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the salary of the group of less than 2 million attendances.
In Sample 2, enter the salary of the group of 2 up to 3 million attendances.
In Sample 3, enter the salary of the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 4

From the above output, the F test statistic value is 24.31 and the p-value is 0.

Conclusion:

The level of significance is 0.05 and the p-value is less than the significance level. Hence, one can reject the null hypothesis at the 0.05 significance level. Thus, the mean salaries are different for each group.

Answer 28

d.

To determine

Find whether there is a difference in the mean salary of the three groups.

Answer 29

d.

Expert Solution

Answer to Problem 50DE

The mean salaries are different for each group.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

The null and alternative hypotheses are stated below:

Null hypothesis: The mean salary of the three groups is equal.

Alternative hypothesis: At least one mean salary is different from other.

The following table provides the salary of each group that is defined in Part b.

Sample 1	Sample 2	Sample 3
96.9	74.3	173.2
78.4	83.3	132.3
60.7	81.4	154.5
60.9	88.2	95.1
55.4	82.2	198
82	78.1	174.5
64.2	118.1	117.6
	97.7	110.3
	94.1	120.5
	93.4
	63.4
	55.2
	75.5
	81.3

Step-by-step procedure to obtain the test statistic using Excel:

In Sample 1, enter the salary of the group of less than 2 million attendances.
In Sample 2, enter the salary of the group of 2 up to 3 million attendances.
In Sample 3, enter the salary of the group of 3 or more million attendances.
Select the Data tab on the top menu.
Select Data Analysis and Click on: ANOVA: Single factor and then click on OK.
In the dialog box, select Input Range.
Click OK

Output obtained using Excel is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 50DE , additional homework tip 4

From the above output, the F test statistic value is 24.31 and the p-value is 0.

Conclusion:

The level of significance is 0.05 and the p-value is less than the significance level. Hence, one can reject the null hypothesis at the 0.05 significance level. Thus, the mean salaries are different for each group.

Answer 34

Ch. 12 - Steele Electric Products Inc. assembles cell...Ch. 12 - What is the critical F value when the sample size...Ch. 12 - Prob. 2E Ch. 12 - Prob. 3E Ch. 12 - Prob. 4E Ch. 12 - Prob. 5E Ch. 12 - Prob. 6E Ch. 12 - Prob. 2SR Ch. 12 - Prob. 7E Ch. 12 - Prob. 8E

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

Concept explainers

Videos

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

Answer to Problem 50DE

Explanation of Solution

Create a variable that classifies a team’s total attendance into three groups.

Find whether there is a difference in the mean number of games won among the three groups.

Answer to Problem 50DE

Explanation of Solution

Find whether there is a difference in the mean number of home runs hit per team using the variable defined in Part b.

Answer to Problem 50DE

Explanation of Solution

Find whether there is a difference in the mean salary of the three groups.

Answer to Problem 50DE

Explanation of Solution

Want to see more full solutions like this?

Chapter 12 Solutions

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

Concept explainers

Videos

Find whether there is a difference in the variation in team salary among the people from Country A and National league teams.

Answer to Problem 50DE

Explanation of Solution

Create a variable that classifies a team’s total attendance into three groups. Find whether there is a difference in the mean number of games won among the three groups.

Answer to Problem 50DE

Explanation of Solution

Find whether there is a difference in the mean number of home runs hit per team using the variable defined in Part b.

Answer to Problem 50DE

Explanation of Solution

Find whether there is a difference in the mean salary of the three groups.

Answer to Problem 50DE

Explanation of Solution

Want to see more full solutions like this?

Chapter 12 Solutions

Create a variable that classifies a team’s total attendance into three groups.

Find whether there is a difference in the mean number of games won among the three groups.