# Expert Answers

10.55 Consider an experiment with four groups, with eight values in each. For the ANOVA summary table below, fill in all the missing results:

Source Degrees of Freedom Sum of Sqrs Mean Square F (Variance)

Among Groups c - 1= ? SSA = ? MSA = 80 FSTAT = ?

Within Groups n - c = ? SSW = 560 MSW = ?

Total n - 1 = ? SST = ?

10.57 The Computer Anxiety Rating Scale (CARS) measures an individual’s level of computer anxiety, on a scale from 20 (no anxiety) to 100 (highest level of anxiety). Researchers at MiamiUniversity administered CARS to 172 business students. One of the objectives of the study was to determine whether there are differences in the amount of computer anxiety experienced by students with different majors. They found the following:

Source Degrees of Sum of Mean Square F

Freedom Squares (variance)

Among majors 5 3,172

Within majors 166 21,246

Total 171 24,418

Major n Mean

Marketing 19 44.37

Management 11 43.18

Other 14 42.21

Finance 45 41.8

Accountancy 36 37.56

MIS 47 32.21

a. Complete the ANOVA summary table.

b. At the 0.05 level of significance, is there evidence of a difference in the mean computer anxiety experienced by different majors?

c. If the results in (b) indicate that it is appropriate, use the Tukey-Kramer procedure to determine which majors differ in mean computer anxiety. Discuss your findings.

10.59 A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus and three satellite locations. Management had a business objective of reducing waiting time for emergency room cases that did not require immediate attention. To study this, a random sample of 15 emergency room cases at each location were selected on a particular day, and the waiting time (measured from check-in to when the patient was called into the clinic area) was measured. The results are stored in ERwaiting.

a. At the 0.05 level of significance, is there evidence of a difference in the mean waiting times in the four locations?

b. If appropriate, determine which locations differ in mean waiting time.

c. At the 0.05 level of significance, is there evidence of a difference in the variation in waiting time among the four locations?

10.61 The per-store daily customer count (i.e., the mean number of customers in a store in one day) for a nationwide convenience store chain that operates nearly 10,000 stores has been steady, at 900, for some time. To increase the customer count, the chain is considering cutting prices for coffee beverages. The question to be determined is how much to cut prices to increase the daily customer count without reducing the gross margin on coffee sales too much. You decide to carry out an experiment in a sample of 24 stores where customer counts have been running almost exactly at the national average of 900. In 6 of the stores, the price of a small coffee will now be $0.59, in 6 stores the price of a small coffee will now be $0.69, in 6 stores, the price of a small coffee will now be $0.79, and in 6 stores, the price of a small coffee will now be $0.89.

After four weeks of selling the coffee at the new price, the daily customer count in the stores was recorded and stored in “coffee sales”.

b. If appropriate, determine which prices differ in daily customer counts.

c. At the 0.05 level of significance, is there evidence of a difference in the variation in daily customer count among the different prices?

d. What effect does your result in (c) have on the validity of the results in (a) and (b)?

11.25 Where people turn to for news is different for various age groups. A study indicated where different age groups primarily get their news:

12.1 Fitting a straight line to a set of data yields the following prediction line:

Yi = 2 + 5Xi

a. Interpret the meaning of the Y intercept, b0.

b. Interpret the meaning of the slope, b1.

c. Predict the value of Y for X = 3.

12.4 The marketing manager of a large supermarket chain has the business objective of using shelf space most efficiently. Toward that goal, she would like to use shelf space to predict sales of pet food. Data is collected from a random sample of 12 equal-sized stores, with the following results.

Store Shelf Space, x(Feet) Weekly Sales, y($)

1 5 160

2 5 220

3 5 140

4 10 190

5 10 240

6 10 260

7 15 230

8 15 270

9 15 280

10 20 260

11 20 290

12 20 310

a. Construct a scatterplot

b. Interpret the meaning of the slope, b1, in this problem.

c. Predict the weekly sales of pet food for stores with 8 feet of shelf space for pet food.

12.9 An agent for a residential real estate company has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The

agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:

a. Construct a scatter plot.

b. Use the least-squares method to find the regression coefficients b0 and b1.

c. Interpret the meaning of b0 and b1 in this problem.

d. Predict the monthly rent for an apartment that has 1,000 square feet.

e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?

f. Your friends Jim and Jennifer are considering signing a lease for an apartment in this residential neighborhood. They are trying to decide between two apartments, one with 1,000 square feet for a monthly rent of $1,275 and the other with 1,200 square feet for a monthly rent of $1,425. Based on (a) through (d), which apartment do you think is a better deal?

12.17 In Problem 12.5 on page 441, you used the summated rating to predict the cost of a restaurant meal. For those data, SSR = 6951.3963 and SST = 15890.11

a. Determine the coefficient of determination, and interpret its meaning.

b. Determine the standard error of the estimate.

c. How useful do you think this regression model is for predicting the cost of a restaurant meal?

12.21 In Problem 12.9 on page 442, an agent for a real estate company wanted to predict the monthly rent for apartments, based on the size of the apartment (stored in the file Rent). Using the results of that problem.

a. Determine the coefficient of determination, r2, and interpret its meaning.

b. Determine the standard error of the estimate, and interpret its meaning.

c. How useful do you think this regression model is for predicting the monthly rent?

d. Can you think of other variables that might explain the variation in monthly rent?

12.43 In Problem 12.5 on page 441, you used the summated rating of a restaurant to predict the cost of a meal. The data are stored in Restaurants). Using the results of that problem, and

a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal?

b. Construct a 95% confidence interval estimate of the population slope

Source Degrees of Freedom Sum of Sqrs Mean Square F (Variance)

Among Groups c - 1= ? SSA = ? MSA = 80 FSTAT = ?

Within Groups n - c = ? SSW = 560 MSW = ?

Total n - 1 = ? SST = ?

10.57 The Computer Anxiety Rating Scale (CARS) measures an individual’s level of computer anxiety, on a scale from 20 (no anxiety) to 100 (highest level of anxiety). Researchers at MiamiUniversity administered CARS to 172 business students. One of the objectives of the study was to determine whether there are differences in the amount of computer anxiety experienced by students with different majors. They found the following:

Source Degrees of Sum of Mean Square F

Freedom Squares (variance)

Among majors 5 3,172

Within majors 166 21,246

Total 171 24,418

Major n Mean

Marketing 19 44.37

Management 11 43.18

Other 14 42.21

Finance 45 41.8

Accountancy 36 37.56

MIS 47 32.21

a. Complete the ANOVA summary table.

b. At the 0.05 level of significance, is there evidence of a difference in the mean computer anxiety experienced by different majors?

c. If the results in (b) indicate that it is appropriate, use the Tukey-Kramer procedure to determine which majors differ in mean computer anxiety. Discuss your findings.

10.59 A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus and three satellite locations. Management had a business objective of reducing waiting time for emergency room cases that did not require immediate attention. To study this, a random sample of 15 emergency room cases at each location were selected on a particular day, and the waiting time (measured from check-in to when the patient was called into the clinic area) was measured. The results are stored in ERwaiting.

a. At the 0.05 level of significance, is there evidence of a difference in the mean waiting times in the four locations?

b. If appropriate, determine which locations differ in mean waiting time.

c. At the 0.05 level of significance, is there evidence of a difference in the variation in waiting time among the four locations?

10.61 The per-store daily customer count (i.e., the mean number of customers in a store in one day) for a nationwide convenience store chain that operates nearly 10,000 stores has been steady, at 900, for some time. To increase the customer count, the chain is considering cutting prices for coffee beverages. The question to be determined is how much to cut prices to increase the daily customer count without reducing the gross margin on coffee sales too much. You decide to carry out an experiment in a sample of 24 stores where customer counts have been running almost exactly at the national average of 900. In 6 of the stores, the price of a small coffee will now be $0.59, in 6 stores the price of a small coffee will now be $0.69, in 6 stores, the price of a small coffee will now be $0.79, and in 6 stores, the price of a small coffee will now be $0.89.

After four weeks of selling the coffee at the new price, the daily customer count in the stores was recorded and stored in “coffee sales”.

b. If appropriate, determine which prices differ in daily customer counts.

c. At the 0.05 level of significance, is there evidence of a difference in the variation in daily customer count among the different prices?

d. What effect does your result in (c) have on the validity of the results in (a) and (b)?

11.25 Where people turn to for news is different for various age groups. A study indicated where different age groups primarily get their news:

12.1 Fitting a straight line to a set of data yields the following prediction line:

Yi = 2 + 5Xi

a. Interpret the meaning of the Y intercept, b0.

b. Interpret the meaning of the slope, b1.

c. Predict the value of Y for X = 3.

12.4 The marketing manager of a large supermarket chain has the business objective of using shelf space most efficiently. Toward that goal, she would like to use shelf space to predict sales of pet food. Data is collected from a random sample of 12 equal-sized stores, with the following results.

Store Shelf Space, x(Feet) Weekly Sales, y($)

1 5 160

2 5 220

3 5 140

4 10 190

5 10 240

6 10 260

7 15 230

8 15 270

9 15 280

10 20 260

11 20 290

12 20 310

a. Construct a scatterplot

b. Interpret the meaning of the slope, b1, in this problem.

c. Predict the weekly sales of pet food for stores with 8 feet of shelf space for pet food.

12.9 An agent for a residential real estate company has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The

agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:

a. Construct a scatter plot.

b. Use the least-squares method to find the regression coefficients b0 and b1.

c. Interpret the meaning of b0 and b1 in this problem.

d. Predict the monthly rent for an apartment that has 1,000 square feet.

e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?

f. Your friends Jim and Jennifer are considering signing a lease for an apartment in this residential neighborhood. They are trying to decide between two apartments, one with 1,000 square feet for a monthly rent of $1,275 and the other with 1,200 square feet for a monthly rent of $1,425. Based on (a) through (d), which apartment do you think is a better deal?

12.17 In Problem 12.5 on page 441, you used the summated rating to predict the cost of a restaurant meal. For those data, SSR = 6951.3963 and SST = 15890.11

a. Determine the coefficient of determination, and interpret its meaning.

b. Determine the standard error of the estimate.

c. How useful do you think this regression model is for predicting the cost of a restaurant meal?

12.21 In Problem 12.9 on page 442, an agent for a real estate company wanted to predict the monthly rent for apartments, based on the size of the apartment (stored in the file Rent). Using the results of that problem.

a. Determine the coefficient of determination, r2, and interpret its meaning.

b. Determine the standard error of the estimate, and interpret its meaning.

c. How useful do you think this regression model is for predicting the monthly rent?

d. Can you think of other variables that might explain the variation in monthly rent?

12.43 In Problem 12.5 on page 441, you used the summated rating of a restaurant to predict the cost of a meal. The data are stored in Restaurants). Using the results of that problem, and

a. At the 0.05 level of significance, is there evidence of a linear relationship between the summated rating of a restaurant and the cost of a meal?

b. Construct a 95% confidence interval estimate of the population slope

You'll get a 421.1KB .DOCX file.