To test: Whether the ‘friends on Facebook’ data is skewed or not by using appropriate graph.

Question

Want to see more full solutions like this?

Answer 1

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.1, Problem 28E

(a)

To determine

To test: Whether the ‘friends on Facebook’ data is skewed or not by using appropriate graph.

(a)

Expert Solution

Answer to Problem 28E

Solution: The data is positively skewed.

Explanation of Solution

Graph: To find whether data is skewed or not, the histogram can be drawn. To draw the histogram, follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Graph→Histogram→simple. Then click on ‘Ok’

Step 3: In dialog box that appears select ‘friends on Facebook’ under the field marked as ‘Graph variable’. Then click Ok.

The histogram is as follows;

Introduction to the Practice of Statistics, Chapter 7.1, Problem 28E

Conclusion: In above graph, it can be seen that most of the frequencies are distributed in right hand side of the highest frequency. Hence, the data is positively skewed.

To determine

To explain: The findings.

Expert Solution

Answer to Problem 28E

Solution: The modal value is somewhere between 100 to 200 and most of the frequencies are on the right side of the modal value so the provided data is positively skewed.

Explanation of Solution

The most frequent any value is between 100 and 200 and most of the frequencies are distributed on the right hand side of this so the distribution is positively skewed.

(b)

To determine

To explain: Whether t method should be used to calculate 95% confidence interval for mean.

(b)

Expert Solution

Answer to Problem 28E

Solution: No, t method should be used to calculate confidence interval.

Explanation of Solution

There is an assumption for using t test that the population distribution must be normally distributed. As shown in part (a) the population distribution is not normal. So t method should not be used.

(c)

Section 1:

To determine

To find: The mean number of Facebook friends for sample.

(c)

Section 1:

Expert Solution

Answer to Problem 28E

Solution: The sample mean is 305.8 (approximated to 306) friends.

Explanation of Solution

Calculation: To calculate the sample mean follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friends’.

Step 2: Go to Stat→Basic statistics→Display Discriptive statistics. Then click on ‘Ok’.

Step 3: In dialog box that appears select ‘Number of Facebook friend’ under the field marked as ‘Variables’. Then click on ‘Statistics’.

Step 4: In dialog box that appears select ‘None’ and then ‘Mean’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the mean is 305.8 but number of friends is an integer value. So mean can never be a decimal value. Therefore, the nearest integer value will be 306. Hence the mean number of friend will be 306 friends.

Section 2:

To determine

To find: The standard deviation of Facebook friends for sample.

Section 2:

Expert Solution

Answer to Problem 28E

Solution: The standard deviation is 294.6 (approximated to 295) friends.

Explanation of Solution

Calculation: To calculate the standard deviation follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘standard deviation’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the standard deviation is 294.6 friends but number of friends is an integer value. So it can never be a decimal value and the nearest integer value will be 295. Hence the standard deviation of the number of friends will be 295 friends.

Section 3:

To determine

To find: The standard error of Facebook friends for sample.

Section 3:

Expert Solution

Answer to Problem 28E

Solution: The standard error is 53.8 (approximated to54) friends.

Explanation of Solution

Calculation: To calculate the standard error follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘SE of mean’. Finally, click ‘Ok’ on both dialog boxes.

From Minitab result, the standard error is 53.8 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 54. Hence the standard deviation of the number of friends will be 54 friends.

Section 4:

To determine

To find: The margin of error for Facebook friends.

Section 4:

Expert Solution

Answer to Problem 28E

Solution: The margin of error is 110.005 (approximated to 110) friends.

Explanation of Solution

Calculation: The formula to calculate the margin of error is as follows,

margin of error = tα2×sn

Where α significance level, s is standard deviation of sample and n is sample size.

margin of error = t0.025×sn=2.04523×294.630=110.005

Hence the margin of error is 110.005 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 110. Hence the margin of error will be 110 friends.

(d)

To determine

To find: 95% confidence interval for data of friends on Facebook.

(d)

Expert Solution

Answer to Problem 28E

Solution: The required confidence interval is (195.8, 415.8)_ and it can be approximated as (196, 416)_.

Explanation of Solution

Calculation: The confidence interval is an interval for which there is 95% chances that it contains the population parameter (population mean).

To calculate confidence interval, follow the below mentioned steps in Minitab;

Step 1: Enter the provided data into Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Stat→Basic statistics→1-sample t.

Step 3: In the dialog box that appears select ‘Number of Facebook friends’ under the field marked as ‘Sample in columns’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘not equal’ in ‘Alternative hypothesis’.

From Minitab results 95% confidence interval is (195.8, 415.8). but the number of friends is an integer value. So the limits of confidence interval can never be a decimal value. Hence the nearest integer value will be 196 and 416. Therefore, the confidence interval of the number of friends will be (196, 416)_.

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

A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…

Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127

Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.1, Problem 28E

(a)

To determine

To test: Whether the ‘friends on Facebook’ data is skewed or not by using appropriate graph.

(a)

Expert Solution

Answer to Problem 28E

Solution: The data is positively skewed.

Explanation of Solution

Graph: To find whether data is skewed or not, the histogram can be drawn. To draw the histogram, follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Graph→Histogram→simple. Then click on ‘Ok’

Step 3: In dialog box that appears select ‘friends on Facebook’ under the field marked as ‘Graph variable’. Then click Ok.

The histogram is as follows;

Introduction to the Practice of Statistics, Chapter 7.1, Problem 28E

Conclusion: In above graph, it can be seen that most of the frequencies are distributed in right hand side of the highest frequency. Hence, the data is positively skewed.

To determine

To explain: The findings.

Expert Solution

Answer to Problem 28E

Solution: The modal value is somewhere between 100 to 200 and most of the frequencies are on the right side of the modal value so the provided data is positively skewed.

Explanation of Solution

The most frequent any value is between 100 and 200 and most of the frequencies are distributed on the right hand side of this so the distribution is positively skewed.

(b)

To determine

To explain: Whether t method should be used to calculate 95% confidence interval for mean.

(b)

Expert Solution

Answer to Problem 28E

Solution: No, t method should be used to calculate confidence interval.

Explanation of Solution

There is an assumption for using t test that the population distribution must be normally distributed. As shown in part (a) the population distribution is not normal. So t method should not be used.

(c)

Section 1:

To determine

To find: The mean number of Facebook friends for sample.

(c)

Section 1:

Expert Solution

Answer to Problem 28E

Solution: The sample mean is 305.8 (approximated to 306) friends.

Explanation of Solution

Calculation: To calculate the sample mean follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friends’.

Step 2: Go to Stat→Basic statistics→Display Discriptive statistics. Then click on ‘Ok’.

Step 3: In dialog box that appears select ‘Number of Facebook friend’ under the field marked as ‘Variables’. Then click on ‘Statistics’.

Step 4: In dialog box that appears select ‘None’ and then ‘Mean’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the mean is 305.8 but number of friends is an integer value. So mean can never be a decimal value. Therefore, the nearest integer value will be 306. Hence the mean number of friend will be 306 friends.

Section 2:

To determine

To find: The standard deviation of Facebook friends for sample.

Section 2:

Expert Solution

Answer to Problem 28E

Solution: The standard deviation is 294.6 (approximated to 295) friends.

Explanation of Solution

Calculation: To calculate the standard deviation follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘standard deviation’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the standard deviation is 294.6 friends but number of friends is an integer value. So it can never be a decimal value and the nearest integer value will be 295. Hence the standard deviation of the number of friends will be 295 friends.

Section 3:

To determine

To find: The standard error of Facebook friends for sample.

Section 3:

Expert Solution

Answer to Problem 28E

Solution: The standard error is 53.8 (approximated to54) friends.

Explanation of Solution

Calculation: To calculate the standard error follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘SE of mean’. Finally, click ‘Ok’ on both dialog boxes.

From Minitab result, the standard error is 53.8 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 54. Hence the standard deviation of the number of friends will be 54 friends.

Section 4:

To determine

To find: The margin of error for Facebook friends.

Section 4:

Expert Solution

Answer to Problem 28E

Solution: The margin of error is 110.005 (approximated to 110) friends.

Explanation of Solution

Calculation: The formula to calculate the margin of error is as follows,

margin of error = tα2×sn

Where α significance level, s is standard deviation of sample and n is sample size.

margin of error = t0.025×sn=2.04523×294.630=110.005

Hence the margin of error is 110.005 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 110. Hence the margin of error will be 110 friends.

(d)

To determine

To find: 95% confidence interval for data of friends on Facebook.

(d)

Expert Solution

Answer to Problem 28E

Solution: The required confidence interval is (195.8, 415.8)_ and it can be approximated as (196, 416)_.

Explanation of Solution

Calculation: The confidence interval is an interval for which there is 95% chances that it contains the population parameter (population mean).

To calculate confidence interval, follow the below mentioned steps in Minitab;

Step 1: Enter the provided data into Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Stat→Basic statistics→1-sample t.

Step 3: In the dialog box that appears select ‘Number of Facebook friends’ under the field marked as ‘Sample in columns’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘not equal’ in ‘Alternative hypothesis’.

From Minitab results 95% confidence interval is (195.8, 415.8). but the number of friends is an integer value. So the limits of confidence interval can never be a decimal value. Hence the nearest integer value will be 196 and 416. Therefore, the confidence interval of the number of friends will be (196, 416)_.

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

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.1, Problem 28E

(a)

To determine

To test: Whether the ‘friends on Facebook’ data is skewed or not by using appropriate graph.

(a)

Expert Solution

Answer to Problem 28E

Solution: The data is positively skewed.

Explanation of Solution

Graph: To find whether data is skewed or not, the histogram can be drawn. To draw the histogram, follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Graph→Histogram→simple. Then click on ‘Ok’

Step 3: In dialog box that appears select ‘friends on Facebook’ under the field marked as ‘Graph variable’. Then click Ok.

The histogram is as follows;

Introduction to the Practice of Statistics, Chapter 7.1, Problem 28E

Conclusion: In above graph, it can be seen that most of the frequencies are distributed in right hand side of the highest frequency. Hence, the data is positively skewed.

To determine

To explain: The findings.

Expert Solution

Answer to Problem 28E

Solution: The modal value is somewhere between 100 to 200 and most of the frequencies are on the right side of the modal value so the provided data is positively skewed.

Explanation of Solution

The most frequent any value is between 100 and 200 and most of the frequencies are distributed on the right hand side of this so the distribution is positively skewed.

(b)

To determine

To explain: Whether t method should be used to calculate 95% confidence interval for mean.

(b)

Expert Solution

Answer to Problem 28E

Solution: No, t method should be used to calculate confidence interval.

Explanation of Solution

There is an assumption for using t test that the population distribution must be normally distributed. As shown in part (a) the population distribution is not normal. So t method should not be used.

(c)

Section 1:

To determine

To find: The mean number of Facebook friends for sample.

(c)

Section 1:

Expert Solution

Answer to Problem 28E

Solution: The sample mean is 305.8 (approximated to 306) friends.

Explanation of Solution

Calculation: To calculate the sample mean follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friends’.

Step 2: Go to Stat→Basic statistics→Display Discriptive statistics. Then click on ‘Ok’.

Step 3: In dialog box that appears select ‘Number of Facebook friend’ under the field marked as ‘Variables’. Then click on ‘Statistics’.

Step 4: In dialog box that appears select ‘None’ and then ‘Mean’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the mean is 305.8 but number of friends is an integer value. So mean can never be a decimal value. Therefore, the nearest integer value will be 306. Hence the mean number of friend will be 306 friends.

Section 2:

To determine

To find: The standard deviation of Facebook friends for sample.

Section 2:

Expert Solution

Answer to Problem 28E

Solution: The standard deviation is 294.6 (approximated to 295) friends.

Explanation of Solution

Calculation: To calculate the standard deviation follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘standard deviation’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the standard deviation is 294.6 friends but number of friends is an integer value. So it can never be a decimal value and the nearest integer value will be 295. Hence the standard deviation of the number of friends will be 295 friends.

Section 3:

To determine

To find: The standard error of Facebook friends for sample.

Section 3:

Expert Solution

Answer to Problem 28E

Solution: The standard error is 53.8 (approximated to54) friends.

Explanation of Solution

Calculation: To calculate the standard error follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘SE of mean’. Finally, click ‘Ok’ on both dialog boxes.

From Minitab result, the standard error is 53.8 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 54. Hence the standard deviation of the number of friends will be 54 friends.

Section 4:

To determine

To find: The margin of error for Facebook friends.

Section 4:

Expert Solution

Answer to Problem 28E

Solution: The margin of error is 110.005 (approximated to 110) friends.

Explanation of Solution

Calculation: The formula to calculate the margin of error is as follows,

margin of error = tα2×sn

Where α significance level, s is standard deviation of sample and n is sample size.

margin of error = t0.025×sn=2.04523×294.630=110.005

Hence the margin of error is 110.005 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 110. Hence the margin of error will be 110 friends.

(d)

To determine

To find: 95% confidence interval for data of friends on Facebook.

(d)

Expert Solution

Answer to Problem 28E

Solution: The required confidence interval is (195.8, 415.8)_ and it can be approximated as (196, 416)_.

Explanation of Solution

Calculation: The confidence interval is an interval for which there is 95% chances that it contains the population parameter (population mean).

To calculate confidence interval, follow the below mentioned steps in Minitab;

Step 1: Enter the provided data into Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Stat→Basic statistics→1-sample t.

Step 3: In the dialog box that appears select ‘Number of Facebook friends’ under the field marked as ‘Sample in columns’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘not equal’ in ‘Alternative hypothesis’.

From Minitab results 95% confidence interval is (195.8, 415.8). but the number of friends is an integer value. So the limits of confidence interval can never be a decimal value. Hence the nearest integer value will be 196 and 416. Therefore, the confidence interval of the number of friends will be (196, 416)_.

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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.1, Problem 28E

(a)

To determine

To test: Whether the ‘friends on Facebook’ data is skewed or not by using appropriate graph.

(a)

Expert Solution

Answer to Problem 28E

Solution: The data is positively skewed.

Explanation of Solution

Graph: To find whether data is skewed or not, the histogram can be drawn. To draw the histogram, follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Graph→Histogram→simple. Then click on ‘Ok’

Step 3: In dialog box that appears select ‘friends on Facebook’ under the field marked as ‘Graph variable’. Then click Ok.

The histogram is as follows;

Introduction to the Practice of Statistics, Chapter 7.1, Problem 28E

Conclusion: In above graph, it can be seen that most of the frequencies are distributed in right hand side of the highest frequency. Hence, the data is positively skewed.

To determine

To explain: The findings.

Expert Solution

Answer to Problem 28E

Solution: The modal value is somewhere between 100 to 200 and most of the frequencies are on the right side of the modal value so the provided data is positively skewed.

Explanation of Solution

The most frequent any value is between 100 and 200 and most of the frequencies are distributed on the right hand side of this so the distribution is positively skewed.

(b)

To determine

To explain: Whether t method should be used to calculate 95% confidence interval for mean.

(b)

Expert Solution

Answer to Problem 28E

Solution: No, t method should be used to calculate confidence interval.

Explanation of Solution

There is an assumption for using t test that the population distribution must be normally distributed. As shown in part (a) the population distribution is not normal. So t method should not be used.

(c)

Section 1:

To determine

To find: The mean number of Facebook friends for sample.

(c)

Section 1:

Expert Solution

Answer to Problem 28E

Solution: The sample mean is 305.8 (approximated to 306) friends.

Explanation of Solution

Calculation: To calculate the sample mean follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friends’.

Step 2: Go to Stat→Basic statistics→Display Discriptive statistics. Then click on ‘Ok’.

Step 3: In dialog box that appears select ‘Number of Facebook friend’ under the field marked as ‘Variables’. Then click on ‘Statistics’.

Step 4: In dialog box that appears select ‘None’ and then ‘Mean’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the mean is 305.8 but number of friends is an integer value. So mean can never be a decimal value. Therefore, the nearest integer value will be 306. Hence the mean number of friend will be 306 friends.

Section 2:

To determine

To find: The standard deviation of Facebook friends for sample.

Section 2:

Expert Solution

Answer to Problem 28E

Solution: The standard deviation is 294.6 (approximated to 295) friends.

Explanation of Solution

Calculation: To calculate the standard deviation follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘standard deviation’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the standard deviation is 294.6 friends but number of friends is an integer value. So it can never be a decimal value and the nearest integer value will be 295. Hence the standard deviation of the number of friends will be 295 friends.

Section 3:

To determine

To find: The standard error of Facebook friends for sample.

Section 3:

Expert Solution

Answer to Problem 28E

Solution: The standard error is 53.8 (approximated to54) friends.

Explanation of Solution

Calculation: To calculate the standard error follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘SE of mean’. Finally, click ‘Ok’ on both dialog boxes.

From Minitab result, the standard error is 53.8 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 54. Hence the standard deviation of the number of friends will be 54 friends.

Section 4:

To determine

To find: The margin of error for Facebook friends.

Section 4:

Expert Solution

Answer to Problem 28E

Solution: The margin of error is 110.005 (approximated to 110) friends.

Explanation of Solution

Calculation: The formula to calculate the margin of error is as follows,

margin of error = tα2×sn

Where α significance level, s is standard deviation of sample and n is sample size.

margin of error = t0.025×sn=2.04523×294.630=110.005

Hence the margin of error is 110.005 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 110. Hence the margin of error will be 110 friends.

(d)

To determine

To find: 95% confidence interval for data of friends on Facebook.

(d)

Expert Solution

Answer to Problem 28E

Solution: The required confidence interval is (195.8, 415.8)_ and it can be approximated as (196, 416)_.

Explanation of Solution

Calculation: The confidence interval is an interval for which there is 95% chances that it contains the population parameter (population mean).

To calculate confidence interval, follow the below mentioned steps in Minitab;

Step 1: Enter the provided data into Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Stat→Basic statistics→1-sample t.

Step 3: In the dialog box that appears select ‘Number of Facebook friends’ under the field marked as ‘Sample in columns’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘not equal’ in ‘Alternative hypothesis’.

From Minitab results 95% confidence interval is (195.8, 415.8). but the number of friends is an integer value. So the limits of confidence interval can never be a decimal value. Hence the nearest integer value will be 196 and 416. Therefore, the confidence interval of the number of friends will be (196, 416)_.

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

Chapter 7.1, Problem 28E

(a)

To determine

To test: Whether the ‘friends on Facebook’ data is skewed or not by using appropriate graph.

(a)

Expert Solution

Answer to Problem 28E

Solution: The data is positively skewed.

Explanation of Solution

Graph: To find whether data is skewed or not, the histogram can be drawn. To draw the histogram, follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Graph→Histogram→simple. Then click on ‘Ok’

Step 3: In dialog box that appears select ‘friends on Facebook’ under the field marked as ‘Graph variable’. Then click Ok.

The histogram is as follows;

Introduction to the Practice of Statistics, Chapter 7.1, Problem 28E

Conclusion: In above graph, it can be seen that most of the frequencies are distributed in right hand side of the highest frequency. Hence, the data is positively skewed.

To determine

To explain: The findings.

Expert Solution

Answer to Problem 28E

Solution: The modal value is somewhere between 100 to 200 and most of the frequencies are on the right side of the modal value so the provided data is positively skewed.

Explanation of Solution

The most frequent any value is between 100 and 200 and most of the frequencies are distributed on the right hand side of this so the distribution is positively skewed.

(b)

To determine

To explain: Whether t method should be used to calculate 95% confidence interval for mean.

(b)

Expert Solution

Answer to Problem 28E

Solution: No, t method should be used to calculate confidence interval.

Explanation of Solution

There is an assumption for using t test that the population distribution must be normally distributed. As shown in part (a) the population distribution is not normal. So t method should not be used.

(c)

Section 1:

To determine

To find: The mean number of Facebook friends for sample.

(c)

Section 1:

Expert Solution

Answer to Problem 28E

Solution: The sample mean is 305.8 (approximated to 306) friends.

Explanation of Solution

Calculation: To calculate the sample mean follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friends’.

Step 2: Go to Stat→Basic statistics→Display Discriptive statistics. Then click on ‘Ok’.

Step 3: In dialog box that appears select ‘Number of Facebook friend’ under the field marked as ‘Variables’. Then click on ‘Statistics’.

Step 4: In dialog box that appears select ‘None’ and then ‘Mean’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the mean is 305.8 but number of friends is an integer value. So mean can never be a decimal value. Therefore, the nearest integer value will be 306. Hence the mean number of friend will be 306 friends.

Section 2:

To determine

To find: The standard deviation of Facebook friends for sample.

Section 2:

Expert Solution

Answer to Problem 28E

Solution: The standard deviation is 294.6 (approximated to 295) friends.

Explanation of Solution

Calculation: To calculate the standard deviation follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘standard deviation’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the standard deviation is 294.6 friends but number of friends is an integer value. So it can never be a decimal value and the nearest integer value will be 295. Hence the standard deviation of the number of friends will be 295 friends.

Section 3:

To determine

To find: The standard error of Facebook friends for sample.

Section 3:

Expert Solution

Answer to Problem 28E

Solution: The standard error is 53.8 (approximated to54) friends.

Explanation of Solution

Calculation: To calculate the standard error follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘SE of mean’. Finally, click ‘Ok’ on both dialog boxes.

From Minitab result, the standard error is 53.8 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 54. Hence the standard deviation of the number of friends will be 54 friends.

Section 4:

To determine

To find: The margin of error for Facebook friends.

Section 4:

Expert Solution

Answer to Problem 28E

Solution: The margin of error is 110.005 (approximated to 110) friends.

Explanation of Solution

Calculation: The formula to calculate the margin of error is as follows,

margin of error = tα2×sn

Where α significance level, s is standard deviation of sample and n is sample size.

margin of error = t0.025×sn=2.04523×294.630=110.005

Hence the margin of error is 110.005 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 110. Hence the margin of error will be 110 friends.

(d)

To determine

To find: 95% confidence interval for data of friends on Facebook.

(d)

Expert Solution

Answer to Problem 28E

Solution: The required confidence interval is (195.8, 415.8)_ and it can be approximated as (196, 416)_.

Explanation of Solution

Calculation: The confidence interval is an interval for which there is 95% chances that it contains the population parameter (population mean).

To calculate confidence interval, follow the below mentioned steps in Minitab;

Step 1: Enter the provided data into Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Stat→Basic statistics→1-sample t.

Step 3: In the dialog box that appears select ‘Number of Facebook friends’ under the field marked as ‘Sample in columns’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘not equal’ in ‘Alternative hypothesis’.

From Minitab results 95% confidence interval is (195.8, 415.8). but the number of friends is an integer value. So the limits of confidence interval can never be a decimal value. Hence the nearest integer value will be 196 and 416. Therefore, the confidence interval of the number of friends will be (196, 416)_.

Answer 6

Chapter 7.1, Problem 28E

(a)

To determine

To test: Whether the ‘friends on Facebook’ data is skewed or not by using appropriate graph.

(a)

Expert Solution

Answer to Problem 28E

Solution: The data is positively skewed.

Explanation of Solution

Graph: To find whether data is skewed or not, the histogram can be drawn. To draw the histogram, follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Graph→Histogram→simple. Then click on ‘Ok’

Step 3: In dialog box that appears select ‘friends on Facebook’ under the field marked as ‘Graph variable’. Then click Ok.

The histogram is as follows;

Introduction to the Practice of Statistics, Chapter 7.1, Problem 28E

Conclusion: In above graph, it can be seen that most of the frequencies are distributed in right hand side of the highest frequency. Hence, the data is positively skewed.

Answer 7

Chapter 7.1, Problem 28E

(a)

To determine

To test: Whether the ‘friends on Facebook’ data is skewed or not by using appropriate graph.

Answer 8

(a)

Expert Solution

Answer to Problem 28E

Solution: The data is positively skewed.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Graph: To find whether data is skewed or not, the histogram can be drawn. To draw the histogram, follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Graph→Histogram→simple. Then click on ‘Ok’

Step 3: In dialog box that appears select ‘friends on Facebook’ under the field marked as ‘Graph variable’. Then click Ok.

The histogram is as follows;

Introduction to the Practice of Statistics, Chapter 7.1, Problem 28E

Conclusion: In above graph, it can be seen that most of the frequencies are distributed in right hand side of the highest frequency. Hence, the data is positively skewed.

Answer 13

To determine

To explain: The findings.

Expert Solution

Answer to Problem 28E

Solution: The modal value is somewhere between 100 to 200 and most of the frequencies are on the right side of the modal value so the provided data is positively skewed.

Explanation of Solution

The most frequent any value is between 100 and 200 and most of the frequencies are distributed on the right hand side of this so the distribution is positively skewed.

Answer 14

To determine

To explain: The findings.

Answer 15

Expert Solution

Answer to Problem 28E

Solution: The modal value is somewhere between 100 to 200 and most of the frequencies are on the right side of the modal value so the provided data is positively skewed.

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The most frequent any value is between 100 and 200 and most of the frequencies are distributed on the right hand side of this so the distribution is positively skewed.

Answer 20

(b)

To determine

To explain: Whether t method should be used to calculate 95% confidence interval for mean.

(b)

Expert Solution

Answer to Problem 28E

Solution: No, t method should be used to calculate confidence interval.

Explanation of Solution

There is an assumption for using t test that the population distribution must be normally distributed. As shown in part (a) the population distribution is not normal. So t method should not be used.

Answer 21

(b)

To determine

To explain: Whether t method should be used to calculate 95% confidence interval for mean.

Answer 22

(b)

Expert Solution

Answer to Problem 28E

Solution: No, t method should be used to calculate confidence interval.

Answer 23

(b)

Expert Solution

Answer 24

(b)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

There is an assumption for using t test that the population distribution must be normally distributed. As shown in part (a) the population distribution is not normal. So t method should not be used.

Answer 27

(c)

Section 1:

To determine

To find: The mean number of Facebook friends for sample.

(c)

Section 1:

Expert Solution

Answer to Problem 28E

Solution: The sample mean is 305.8 (approximated to 306) friends.

Explanation of Solution

Calculation: To calculate the sample mean follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friends’.

Step 2: Go to Stat→Basic statistics→Display Discriptive statistics. Then click on ‘Ok’.

Step 3: In dialog box that appears select ‘Number of Facebook friend’ under the field marked as ‘Variables’. Then click on ‘Statistics’.

Step 4: In dialog box that appears select ‘None’ and then ‘Mean’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the mean is 305.8 but number of friends is an integer value. So mean can never be a decimal value. Therefore, the nearest integer value will be 306. Hence the mean number of friend will be 306 friends.

Answer 28

(c)

Section 1:

To determine

To find: The mean number of Facebook friends for sample.

Answer 29

(c)

Section 1:

Expert Solution

Answer to Problem 28E

Solution: The sample mean is 305.8 (approximated to 306) friends.

Answer 30

(c)

Section 1:

Expert Solution

Answer 31

(c)

Section 1:

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Calculation: To calculate the sample mean follow the below mentioned steps in Minitab;

Step 1: Enter the data in Minitab and enter variable name as ‘Number of Facebook friends’.

Step 2: Go to Stat→Basic statistics→Display Discriptive statistics. Then click on ‘Ok’.

Step 3: In dialog box that appears select ‘Number of Facebook friend’ under the field marked as ‘Variables’. Then click on ‘Statistics’.

Step 4: In dialog box that appears select ‘None’ and then ‘Mean’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the mean is 305.8 but number of friends is an integer value. So mean can never be a decimal value. Therefore, the nearest integer value will be 306. Hence the mean number of friend will be 306 friends.

Answer 34

Section 2:

To determine

To find: The standard deviation of Facebook friends for sample.

Section 2:

Expert Solution

Answer to Problem 28E

Solution: The standard deviation is 294.6 (approximated to 295) friends.

Explanation of Solution

Calculation: To calculate the standard deviation follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘standard deviation’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the standard deviation is 294.6 friends but number of friends is an integer value. So it can never be a decimal value and the nearest integer value will be 295. Hence the standard deviation of the number of friends will be 295 friends.

Answer 35

Section 2:

To determine

To find: The standard deviation of Facebook friends for sample.

Answer 36

Section 2:

Expert Solution

Answer to Problem 28E

Solution: The standard deviation is 294.6 (approximated to 295) friends.

Answer 37

Section 2:

Expert Solution

Answer 38

Section 2:

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Calculation: To calculate the standard deviation follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘standard deviation’. Finally click ‘Ok’ on both dialog boxes.

From Minitab result, the standard deviation is 294.6 friends but number of friends is an integer value. So it can never be a decimal value and the nearest integer value will be 295. Hence the standard deviation of the number of friends will be 295 friends.

Answer 41

Section 3:

To determine

To find: The standard error of Facebook friends for sample.

Section 3:

Expert Solution

Answer to Problem 28E

Solution: The standard error is 53.8 (approximated to54) friends.

Explanation of Solution

Calculation: To calculate the standard error follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘SE of mean’. Finally, click ‘Ok’ on both dialog boxes.

From Minitab result, the standard error is 53.8 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 54. Hence the standard deviation of the number of friends will be 54 friends.

Answer 42

Section 3:

To determine

To find: The standard error of Facebook friends for sample.

Answer 43

Section 3:

Expert Solution

Answer to Problem 28E

Solution: The standard error is 53.8 (approximated to54) friends.

Answer 44

Section 3:

Expert Solution

Answer 45

Section 3:

Expert Solution

Answer 46

Expert Solution

Answer 47

Explanation of Solution

Calculation: To calculate the standard error follow the below mentioned steps in Minitab;

Step 1: Follow the step 1 to 3 performed in section 1 of part (b).

Step 2: In dialog box that appears select ‘None’ and then ‘SE of mean’. Finally, click ‘Ok’ on both dialog boxes.

From Minitab result, the standard error is 53.8 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 54. Hence the standard deviation of the number of friends will be 54 friends.

Answer 48

Section 4:

To determine

To find: The margin of error for Facebook friends.

Section 4:

Expert Solution

Answer to Problem 28E

Solution: The margin of error is 110.005 (approximated to 110) friends.

Explanation of Solution

Calculation: The formula to calculate the margin of error is as follows,

margin of error = tα2×sn

Where α significance level, s is standard deviation of sample and n is sample size.

margin of error = t0.025×sn=2.04523×294.630=110.005

Hence the margin of error is 110.005 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 110. Hence the margin of error will be 110 friends.

Answer 49

Section 4:

To determine

To find: The margin of error for Facebook friends.

Answer 50

Section 4:

Expert Solution

Answer to Problem 28E

Solution: The margin of error is 110.005 (approximated to 110) friends.

Answer 51

Section 4:

Expert Solution

Answer 52

Section 4:

Expert Solution

Answer 53

Expert Solution

Answer 54

Explanation of Solution

Calculation: The formula to calculate the margin of error is as follows,

margin of error = tα2×sn

Where α significance level, s is standard deviation of sample and n is sample size.

margin of error = t0.025×sn=2.04523×294.630=110.005

Hence the margin of error is 110.005 friends but the number of friends is an integer value. So the standard error can never be a decimal value. Therefore, the nearest integer value will be 110. Hence the margin of error will be 110 friends.

Answer 55

(d)

To determine

To find: 95% confidence interval for data of friends on Facebook.

(d)

Expert Solution

Answer to Problem 28E

Solution: The required confidence interval is (195.8, 415.8)_ and it can be approximated as (196, 416)_.

Explanation of Solution

Calculation: The confidence interval is an interval for which there is 95% chances that it contains the population parameter (population mean).

To calculate confidence interval, follow the below mentioned steps in Minitab;

Step 1: Enter the provided data into Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Stat→Basic statistics→1-sample t.

Step 3: In the dialog box that appears select ‘Number of Facebook friends’ under the field marked as ‘Sample in columns’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘not equal’ in ‘Alternative hypothesis’.

From Minitab results 95% confidence interval is (195.8, 415.8). but the number of friends is an integer value. So the limits of confidence interval can never be a decimal value. Hence the nearest integer value will be 196 and 416. Therefore, the confidence interval of the number of friends will be (196, 416)_.

Answer 56

(d)

To determine

To find: 95% confidence interval for data of friends on Facebook.

Answer 57

(d)

Expert Solution

Answer to Problem 28E

Solution: The required confidence interval is (195.8, 415.8)_ and it can be approximated as (196, 416)_.

Answer 58

(d)

Expert Solution

Answer 59

(d)

Expert Solution

Answer 60

Expert Solution

Answer 61

Explanation of Solution

Calculation: The confidence interval is an interval for which there is 95% chances that it contains the population parameter (population mean).

To calculate confidence interval, follow the below mentioned steps in Minitab;

Step 1: Enter the provided data into Minitab and enter variable name as ‘Number of Facebook friend’.

Step 2: Go to Stat→Basic statistics→1-sample t.

Step 3: In the dialog box that appears select ‘Number of Facebook friends’ under the field marked as ‘Sample in columns’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘not equal’ in ‘Alternative hypothesis’.

From Minitab results 95% confidence interval is (195.8, 415.8). but the number of friends is an integer value. So the limits of confidence interval can never be a decimal value. Hence the nearest integer value will be 196 and 416. Therefore, the confidence interval of the number of friends will be (196, 416)_.