Calculus and Above

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Please complete all problems in excel spreadsheet using all required formats as noted.

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 Squares Mean Square (Variance) F

Among c - 1 =? SSA =? MSA = 80 F stat =?

groups

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

groups

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 Miami University 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 Freedom Sum of Squares Mean Squares F

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 41.80

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?

NOTICE Exercises 10.59 and 10.61 require the use of the "One-Way ANOVA" function within the Data Analysis menu in Excel.

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 the file ERwaiting.

Main Satellite 1 Satellite 2 Satellite 3

120.08 30.75 75.86 54.05

81.90 61.83 37.88 38.82

78.79 26.40 68.73 36.85

63.83 53.84 51.08 32.83

79.77 72. 30 50.21 52.94

47.94 53.09 58.47 34.13

79.88 27.67 86.29 69.37

48.63 52.46 62.90 78.52

55.43 10.64 44.84 55.95

64.06 53.50 64.17 49.61

64.99 37.28 50.68 66.40

53.82 34.31 47.97 76.06

62.43 66.00 60.57 11.37

65.07 8.99 58.37 83.51

81.02 29.75 30.40 39.17

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

10.61 The following data (stored in the file CDyield) represent the nationwide highest yield of different types of accounts (extracted from Bankrate.com, March 31, 2008):

Money Market Six Month CD One-Year CD 2.5 Year CD Five Year CD

4.00 3.85 4.05 3.80 4.30

3.82 3.60 3.61 3.70 4.15

3.80 3.60 3.60 3.51 4.10

3.75 3.45 3.60 3.35 4.00

3.75 3.43 3.50 3.35 4.00

a. At the 0.05 level of significance, is there evidence of a difference in the mean yields of the different accounts?

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:

AGE GROUPS

MEDIA Under 36 36–50 50+

Local TV 107 119 133

National TV 73 102 127

Radio 75 97 109

Local newspaper 52 79 107

Internet 95 83 76

At the 0.05 level of significance, is there evidence of a significant relationship between the age group and where people primarily get their news? If so, explain the relationship.

Complete exercises 12.1, 12.5, 12.9, 12.17, 12.21, For 12.43 (assume "Calories" is the "x" variable and "Fat" is the "y" variable) Exercises 12.17, 12.21, and 12.43 require the use of the "Regression" function within the Data Analysis menu in Excel. Refer to Appendix E12 for instructions on using Excel for these exercises.

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

Ŷ i =2+ 5Xi

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

b. Interpret the meaning of the slope, b1.

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

12.5 Circulation is the lifeblood of the publishing business. The larger the sales of a magazine, the more it can charge advertisers. Recently, a circulation gap has appeared between the publishers’ reports of magazines’ newsstand sales and subsequent audits by the Audit Bureau of Circulations. The data in the file Circulation represent the reported and audited newsstand yearly sales (in thousands) for the following 10 magazines:

Magazine Reported (X) Audited (Y)

YM 621.0 299.6

CosmoGirl 359.7 207.7

Rosie 530.0 325.0

Playboy 492.1 336.3

Esquire 70.5 48.6

TeenPeople 567.0 400.3

More 125.5 91.2

Spin 50.6 39.1

Vogue 353.3 268.6

Elle 263.6 214.3

a.Construct a scatter plot.

For this data, bₒ = 26.724 and b1 =0.5719

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

c.Predict the audited newsstand sales of 400,000

12.9 An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of the apartment, as defined by square footage. A sample of 25 apartments (stored in the file Rent) in a particular residential neighborhood was selected, and the information gathered revealed the following:

Rent Size

950 850

1600 1450

1200 1085

1500 1232

950 718

1700 1485

1650 1136

935 726

875 700

1150 956

1400 1100

1650 1285

2300 1985

1800 1369

1400 1175

1450 1225

1100 1245

1700 1259

1200 1150

1150 896

1600 1361

1650 1040

1200 755 (NNN) NNN-NNNN

1750 1200

a. Construct a scatter plot.

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

c. Interpret the meaning of bₒ 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 417, you used reported magazine newsstand sales to predict audited sales (stored in the file Circulation).

For that data, SSR = 130,301.41 and SST = 144,538.64.

Magazine Reported Audited

YM 621.0 299.6

CosmoGirl 359.7 207.7

Rosie 530. 0 325.0

Playboy 492.1 336.3

Esquire 70.5 48.6

TeenPeople 567.0 400.3

More 125.5 91.2

Spin 50.6 39.1

Vogue 353.3 268.6

Elle 263.6 214.3

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

b. Determine the standard error of the estimate.

c. How useful do you think this regression model is for predicting audited sales?

12.21 In Problem 12.9 on page 418, 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 in monthly rent?

12.43 The data in the file Coffeedrink represent the calories and fat (in grams) of 16-ounce iced coffee drinks at Dunkin’ Donuts and Starbucks:

Product Calories Fat

Dunkin' Donuts Iced Mocha Swirl latte (whole milk) 240 8.0

Starbucks Coffee Frappuccino blended coffee 260 3.5

Dunkin' Donuts Coffee Coolatta (cream) 350 22.0

Starbucks Iced Coffee Mocha Expresso (whole milk and whipped cream 350 20.0

Starbucks Mocha Frappuccino blended coffee (whipped cream) 420 16.0

Starbucks Chocolate Brownie Frappuccino blended coffee (whipped cream) 510 22.0

Starbucks Chocolate Frappuccino Blended Crème (whipped cream) 530 19.0

a. Compute and interpret the coefficient of correlation, r.

b. At the 0.05 level of significance, is there a significant linear relationship between calories and fat?

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 Squares Mean Square (Variance) F

Among c - 1 =? SSA =? MSA = 80 F stat =?

groups

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

groups

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 Miami University 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 Freedom Sum of Squares Mean Squares F

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 41.80

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?

NOTICE Exercises 10.59 and 10.61 require the use of the "One-Way ANOVA" function within the Data Analysis menu in Excel.

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 the file ERwaiting.

Main Satellite 1 Satellite 2 Satellite 3

120.08 30.75 75.86 54.05

81.90 61.83 37.88 38.82

78.79 26.40 68.73 36.85

63.83 53.84 51.08 32.83

79.77 72. 30 50.21 52.94

47.94 53.09 58.47 34.13

79.88 27.67 86.29 69.37

48.63 52.46 62.90 78.52

55.43 10.64 44.84 55.95

64.06 53.50 64.17 49.61

64.99 37.28 50.68 66.40

53.82 34.31 47.97 76.06

62.43 66.00 60.57 11.37

65.07 8.99 58.37 83.51

81.02 29.75 30.40 39.17

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

10.61 The following data (stored in the file CDyield) represent the nationwide highest yield of different types of accounts (extracted from Bankrate.com, March 31, 2008):

Money Market Six Month CD One-Year CD 2.5 Year CD Five Year CD

4.00 3.85 4.05 3.80 4.30

3.82 3.60 3.61 3.70 4.15

3.80 3.60 3.60 3.51 4.10

3.75 3.45 3.60 3.35 4.00

3.75 3.43 3.50 3.35 4.00

a. At the 0.05 level of significance, is there evidence of a difference in the mean yields of the different accounts?

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:

AGE GROUPS

MEDIA Under 36 36–50 50+

Local TV 107 119 133

National TV 73 102 127

Radio 75 97 109

Local newspaper 52 79 107

Internet 95 83 76

At the 0.05 level of significance, is there evidence of a significant relationship between the age group and where people primarily get their news? If so, explain the relationship.

Complete exercises 12.1, 12.5, 12.9, 12.17, 12.21, For 12.43 (assume "Calories" is the "x" variable and "Fat" is the "y" variable) Exercises 12.17, 12.21, and 12.43 require the use of the "Regression" function within the Data Analysis menu in Excel. Refer to Appendix E12 for instructions on using Excel for these exercises.

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

Ŷ i =2+ 5Xi

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

b. Interpret the meaning of the slope, b1.

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

12.5 Circulation is the lifeblood of the publishing business. The larger the sales of a magazine, the more it can charge advertisers. Recently, a circulation gap has appeared between the publishers’ reports of magazines’ newsstand sales and subsequent audits by the Audit Bureau of Circulations. The data in the file Circulation represent the reported and audited newsstand yearly sales (in thousands) for the following 10 magazines:

Magazine Reported (X) Audited (Y)

YM 621.0 299.6

CosmoGirl 359.7 207.7

Rosie 530.0 325.0

Playboy 492.1 336.3

Esquire 70.5 48.6

TeenPeople 567.0 400.3

More 125.5 91.2

Spin 50.6 39.1

Vogue 353.3 268.6

Elle 263.6 214.3

a.Construct a scatter plot.

For this data, bₒ = 26.724 and b1 =0.5719

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

c.Predict the audited newsstand sales of 400,000

12.9 An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of the apartment, as defined by square footage. A sample of 25 apartments (stored in the file Rent) in a particular residential neighborhood was selected, and the information gathered revealed the following:

Rent Size

950 850

1600 1450

1200 1085

1500 1232

950 718

1700 1485

1650 1136

935 726

875 700

1150 956

1400 1100

1650 1285

2300 1985

1800 1369

1400 1175

1450 1225

1100 1245

1700 1259

1200 1150

1150 896

1600 1361

1650 1040

1200 755 (NNN) NNN-NNNN

1750 1200

a. Construct a scatter plot.

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

c. Interpret the meaning of bₒ 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 417, you used reported magazine newsstand sales to predict audited sales (stored in the file Circulation).

For that data, SSR = 130,301.41 and SST = 144,538.64.

Magazine Reported Audited

YM 621.0 299.6

CosmoGirl 359.7 207.7

Rosie 530. 0 325.0

Playboy 492.1 336.3

Esquire 70.5 48.6

TeenPeople 567.0 400.3

More 125.5 91.2

Spin 50.6 39.1

Vogue 353.3 268.6

Elle 263.6 214.3

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

b. Determine the standard error of the estimate.

c. How useful do you think this regression model is for predicting audited sales?

12.21 In Problem 12.9 on page 418, 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 in monthly rent?

12.43 The data in the file Coffeedrink represent the calories and fat (in grams) of 16-ounce iced coffee drinks at Dunkin’ Donuts and Starbucks:

Product Calories Fat

Dunkin' Donuts Iced Mocha Swirl latte (whole milk) 240 8.0

Starbucks Coffee Frappuccino blended coffee 260 3.5

Dunkin' Donuts Coffee Coolatta (cream) 350 22.0

Starbucks Iced Coffee Mocha Expresso (whole milk and whipped cream 350 20.0

Starbucks Mocha Frappuccino blended coffee (whipped cream) 420 16.0

Starbucks Chocolate Brownie Frappuccino blended coffee (whipped cream) 510 22.0

Starbucks Chocolate Frappuccino Blended Crème (whipped cream) 530 19.0

a. Compute and interpret the coefficient of correlation, r.

b. At the 0.05 level of significance, is there a significant linear relationship between calories and fat?

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