Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a .05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?

Question

Want to see more full solutions like this?

Answer 1

Textbook Question

Chapter 13, Problem 34E

Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a .05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?

Chapter 13, Problem 34E, Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels

Expert Solution & Answer

To determine

Check whether there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer to Problem 34E

Yes, there appears to be a difference in the ability of the brands to absorb water.

Explanation of Solution

Calculation:

The data represents the absorbency rate for the three brands.

Assume that, μ1, μ2 and μ3 denote the population means of three brands x, y and z respectively.

The test hypotheses are given below:

Null hypothesis:

H0:μ1=μ2=μ3

Alternative hypothesis:

Ha: At least one of the means is not equal.

It is given that the level of significance as 0.05.

One-way Anova:

Software procedure:

Step-by-step procedure to obtain One-way Anova using the EXCEL:

Enter the data in an EXCEL sheet.
On Data tab in Analysis group, click Data Analysis.
Select Anova: Single Factor.
Click Ok.
Click in the Input Range box, select the range $A$1: $C$5.
Click in the Output range, select $G$1
Click OK.

Output using the EXCEL software is given below:

Essentials Of Statistics For Business & Economics, Chapter 13, Problem 34E

From the EXCEL output, the F-ratio is 7.23 and the p-value is 0.0134.

Decision:

If p-value≤α, reject the null hypothesis H0.

If p-value>α, fail to reject the null hypothesis H0.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.0134)<α(=0.05).

Therefore, the null hypothesis is rejected.

Hence, there is sufficient evidence to infer that there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

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!

Students have asked these similar questions

I just need to know why this is wrong below: What is the test statistic W? W=5 (incorrect) and What is the p-value of this test? (p-value < 0.001-- incorrect) Use the Wilcoxon signed rank test to test the hypothesis that the median number of pages in the statistics books in the library from which the sample was taken is 400. A sample of 12 statistics books have the following numbers of pages pages 127 217 486 132 397 297 396 327 292 256 358 272 What is the sum of the negative ranks (W-)? 75 What is the sum of the positive ranks (W+)? 5What type of test is this? two tailedWhat is the test statistic W? 5 These are the critical values for a 1-tailed Wilcoxon Signed Rank test for n=12 Alpha Level 0.001 0.005 0.01 0.025 0.05 0.1 0.2 Critical Value 75 70 68 64 60 56 50 What is the p-value for this test? p-value < 0.001

ons 12. A sociologist hypothesizes that the crime rate is higher in areas with higher poverty rate and lower median income. She col- lects data on the crime rate (crimes per 100,000 residents), the poverty rate (in %), and the median income (in $1,000s) from 41 New England cities. A portion of the regression results is shown in the following table. Standard Coefficients error t stat p-value Intercept -301.62 549.71 -0.55 0.5864 Poverty 53.16 14.22 3.74 0.0006 Income 4.95 8.26 0.60 0.5526 a. b. Are the signs as expected on the slope coefficients? Predict the crime rate in an area with a poverty rate of 20% and a median income of $50,000. 3. Using data from 50 work

2. The owner of several used-car dealerships believes that the selling price of a used car can best be predicted using the car's age. He uses data on the recent selling price (in $) and age of 20 used sedans to estimate Price = Po + B₁Age + ε. A portion of the regression results is shown in the accompanying table. Standard Coefficients Intercept 21187.94 Error 733.42 t Stat p-value 28.89 1.56E-16 Age -1208.25 128.95 -9.37 2.41E-08 a. What is the estimate for B₁? Interpret this value. b. What is the sample regression equation? C. Predict the selling price of a 5-year-old sedan.

Answer 2

Textbook Question

Chapter 13, Problem 34E

Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a .05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?

Chapter 13, Problem 34E, Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels

Expert Solution & Answer

To determine

Check whether there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer to Problem 34E

Yes, there appears to be a difference in the ability of the brands to absorb water.

Explanation of Solution

Calculation:

The data represents the absorbency rate for the three brands.

Assume that, μ1, μ2 and μ3 denote the population means of three brands x, y and z respectively.

The test hypotheses are given below:

Null hypothesis:

H0:μ1=μ2=μ3

Alternative hypothesis:

Ha: At least one of the means is not equal.

It is given that the level of significance as 0.05.

One-way Anova:

Software procedure:

Step-by-step procedure to obtain One-way Anova using the EXCEL:

Enter the data in an EXCEL sheet.
On Data tab in Analysis group, click Data Analysis.
Select Anova: Single Factor.
Click Ok.
Click in the Input Range box, select the range $A$1: $C$5.
Click in the Output range, select $G$1
Click OK.

Output using the EXCEL software is given below:

Essentials Of Statistics For Business & Economics, Chapter 13, Problem 34E

From the EXCEL output, the F-ratio is 7.23 and the p-value is 0.0134.

Decision:

If p-value≤α, reject the null hypothesis H0.

If p-value>α, fail to reject the null hypothesis H0.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.0134)<α(=0.05).

Therefore, the null hypothesis is rejected.

Hence, there is sufficient evidence to infer that there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

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 3

Textbook Question

Chapter 13, Problem 34E

Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a .05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?

Chapter 13, Problem 34E, Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels

Expert Solution & Answer

To determine

Check whether there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer to Problem 34E

Yes, there appears to be a difference in the ability of the brands to absorb water.

Explanation of Solution

Calculation:

The data represents the absorbency rate for the three brands.

Assume that, μ1, μ2 and μ3 denote the population means of three brands x, y and z respectively.

The test hypotheses are given below:

Null hypothesis:

H0:μ1=μ2=μ3

Alternative hypothesis:

Ha: At least one of the means is not equal.

It is given that the level of significance as 0.05.

One-way Anova:

Software procedure:

Step-by-step procedure to obtain One-way Anova using the EXCEL:

Enter the data in an EXCEL sheet.
On Data tab in Analysis group, click Data Analysis.
Select Anova: Single Factor.
Click Ok.
Click in the Input Range box, select the range $A$1: $C$5.
Click in the Output range, select $G$1
Click OK.

Output using the EXCEL software is given below:

Essentials Of Statistics For Business & Economics, Chapter 13, Problem 34E

From the EXCEL output, the F-ratio is 7.23 and the p-value is 0.0134.

Decision:

If p-value≤α, reject the null hypothesis H0.

If p-value>α, fail to reject the null hypothesis H0.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.0134)<α(=0.05).

Therefore, the null hypothesis is rejected.

Hence, there is sufficient evidence to infer that there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

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

Textbook Question

Chapter 13, Problem 34E

Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a .05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?

Chapter 13, Problem 34E, Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels

Expert Solution & Answer

To determine

Check whether there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer to Problem 34E

Yes, there appears to be a difference in the ability of the brands to absorb water.

Explanation of Solution

Calculation:

The data represents the absorbency rate for the three brands.

Assume that, μ1, μ2 and μ3 denote the population means of three brands x, y and z respectively.

The test hypotheses are given below:

Null hypothesis:

H0:μ1=μ2=μ3

Alternative hypothesis:

Ha: At least one of the means is not equal.

It is given that the level of significance as 0.05.

One-way Anova:

Software procedure:

Step-by-step procedure to obtain One-way Anova using the EXCEL:

Enter the data in an EXCEL sheet.
On Data tab in Analysis group, click Data Analysis.
Select Anova: Single Factor.
Click Ok.
Click in the Input Range box, select the range $A$1: $C$5.
Click in the Output range, select $G$1
Click OK.

Output using the EXCEL software is given below:

Essentials Of Statistics For Business & Economics, Chapter 13, Problem 34E

From the EXCEL output, the F-ratio is 7.23 and the p-value is 0.0134.

Decision:

If p-value≤α, reject the null hypothesis H0.

If p-value>α, fail to reject the null hypothesis H0.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.0134)<α(=0.05).

Therefore, the null hypothesis is rejected.

Hence, there is sufficient evidence to infer that there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

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 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

Check whether there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer to Problem 34E

Yes, there appears to be a difference in the ability of the brands to absorb water.

Explanation of Solution

Calculation:

The data represents the absorbency rate for the three brands.

Assume that, μ1, μ2 and μ3 denote the population means of three brands x, y and z respectively.

The test hypotheses are given below:

Null hypothesis:

H0:μ1=μ2=μ3

Alternative hypothesis:

Ha: At least one of the means is not equal.

It is given that the level of significance as 0.05.

One-way Anova:

Software procedure:

Step-by-step procedure to obtain One-way Anova using the EXCEL:

Enter the data in an EXCEL sheet.
On Data tab in Analysis group, click Data Analysis.
Select Anova: Single Factor.
Click Ok.
Click in the Input Range box, select the range $A$1: $C$5.
Click in the Output range, select $G$1
Click OK.

Output using the EXCEL software is given below:

Essentials Of Statistics For Business & Economics, Chapter 13, Problem 34E

From the EXCEL output, the F-ratio is 7.23 and the p-value is 0.0134.

Decision:

If p-value≤α, reject the null hypothesis H0.

If p-value>α, fail to reject the null hypothesis H0.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.0134)<α(=0.05).

Therefore, the null hypothesis is rejected.

Hence, there is sufficient evidence to infer that there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer 8

Expert Solution & Answer

To determine

Check whether there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer to Problem 34E

Yes, there appears to be a difference in the ability of the brands to absorb water.

Explanation of Solution

Calculation:

The data represents the absorbency rate for the three brands.

Assume that, μ1, μ2 and μ3 denote the population means of three brands x, y and z respectively.

The test hypotheses are given below:

Null hypothesis:

H0:μ1=μ2=μ3

Alternative hypothesis:

Ha: At least one of the means is not equal.

It is given that the level of significance as 0.05.

One-way Anova:

Software procedure:

Step-by-step procedure to obtain One-way Anova using the EXCEL:

Enter the data in an EXCEL sheet.
On Data tab in Analysis group, click Data Analysis.
Select Anova: Single Factor.
Click Ok.
Click in the Input Range box, select the range $A$1: $C$5.
Click in the Output range, select $G$1
Click OK.

Output using the EXCEL software is given below:

Essentials Of Statistics For Business & Economics, Chapter 13, Problem 34E

From the EXCEL output, the F-ratio is 7.23 and the p-value is 0.0134.

Decision:

If p-value≤α, reject the null hypothesis H0.

If p-value>α, fail to reject the null hypothesis H0.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.0134)<α(=0.05).

Therefore, the null hypothesis is rejected.

Hence, there is sufficient evidence to infer that there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

Check whether there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer 12

Answer to Problem 34E

Yes, there appears to be a difference in the ability of the brands to absorb water.

Answer 13

Explanation of Solution

Calculation:

The data represents the absorbency rate for the three brands.

Assume that, μ1, μ2 and μ3 denote the population means of three brands x, y and z respectively.

The test hypotheses are given below:

Null hypothesis:

H0:μ1=μ2=μ3

Alternative hypothesis:

Ha: At least one of the means is not equal.

It is given that the level of significance as 0.05.

One-way Anova:

Software procedure:

Step-by-step procedure to obtain One-way Anova using the EXCEL:

Enter the data in an EXCEL sheet.
On Data tab in Analysis group, click Data Analysis.
Select Anova: Single Factor.
Click Ok.
Click in the Input Range box, select the range $A$1: $C$5.
Click in the Output range, select $G$1
Click OK.

Output using the EXCEL software is given below:

Essentials Of Statistics For Business & Economics, Chapter 13, Problem 34E

From the EXCEL output, the F-ratio is 7.23 and the p-value is 0.0134.

Decision:

If p-value≤α, reject the null hypothesis H0.

If p-value>α, fail to reject the null hypothesis H0.

Conclusion:

Here, the p-value is less than the level of significance.

That is, p-value(=0.0134)<α(=0.05).

Therefore, the null hypothesis is rejected.

Hence, there is sufficient evidence to infer that there is a significant difference among the mean absorbency ratings for the three brands at α=0.05 level of significance.

Answer 14

Ch. 13.2 - The following data are from a completely...Ch. 13.2 - 2. In a completely randomized design, seven...Ch. 13.2 - 3. Refer to exercise 2. what hypotheses are...Ch. 13.2 - 4. In an experiment designed to test the output...Ch. 13.2 - 5. In a completely randomized design, 12...Ch. 13.2 - Develop the analysis of variance computations for...Ch. 13.2 - 7. Three different methods for assembling a...Ch. 13.2 - 8. Refer to the NCP data in Table 13.4. Set up the...Ch. 13.2 - To study the effect of temperature on yield in a...Ch. 13.2 - Prob. 10E

Videos

Answer to Problem 34E

Explanation of Solution

Want to see more full solutions like this?

Chapter 13 Solutions