Problem set 8

problem_set_8.xlsx

1 0

.

5

5

reedom

Square (Variance)

F

.

Consider an experiment with four groups, with eight

each. For the ANOVA summary table below, fill in

Source

Degrees of

F

Sum of Squares

Mea

n

10

55

Among Groups

c – 1 = ?

SSA = ?

MSA = 80

FSTAT = ?

values

in

Within Groups

n – c = ?

SSW = 5

60

MSW = ?

all the missing results:

Total

n – 1 = ?

SST = ?

10.

57

Source

Squares

F

s

5

2

6

6

(no anxiety) to 100 (highest level of anxiety).

Total

Major n Mean

.18

.21

.8

.21

Degree of Freedom	Sum of Squares		Mean	10.57 The Computer Anxiety Rating Scale (CARS) measures
Among	Major	3																																																		17	an individual’s level of computer anxiety, on a scale
Within Majors																																					16																																																																									21																																								24	from																																																																																			20
171	2														44																																																														18	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
Marketing																																																																																	19	44.										37	computer anxiety experienced by students with different majors.
Management									11											43	They found the following:
Other											14											42
Finance									45							41	a. Complete the ANOVA summary table.
Accountancy			36	37.																		56	b.	At the 0.05 level of significance, is there evidence of a
MIS	47							32	difference in the mean computer anxiety experienced by
different majors?

10.

59

ERWaiting

0.08

.

.05

.

.82

.

.

.

.83

.84

.08

.21

.94

emergency room cases that did not require immediate

.47

.

.

.37

.63

.90

.61

.40

.06

.07

.17

Main	Satellite 1	Satellite 2	Satellite 3	10.59 A hospital conducted a study of the waiting time in		require the use of the “One-Way ANOVA”
										12			30			75	75.86													54	its emergency room. The hospital has a main campus and
81.90													61	83	37.88							38	three satellite locations. Management had a business objective
		78					79									26										40													68			73	36.85	of reducing waiting time for emergency room cases that
						63													53													51	32.83	did not require immediate attention. To study this, a random
79.77	72.30									50										52	sample of																							15
47.94	53.09									58							34								13	attention at each location were selected on a particular
79.88									27						67	86.						29					69	day, and the waiting time (measured from check-in to
												48	52.						46											62	78.52	when the patient was called into the clinic area) was measured.
55.43	10.																		64	44.84	55.	95	The results are stored in
64.06	53.50	64.17													49
64.99	37.				28	50.68							66
		a. At the 0.05 level of significance, is there evidence of a
53.82	34.		31	47.	97		76	difference in the mean waiting times in the four locations?
62.43	66.00	60.57	11.37
												65	8.99	58.37	83.51
81.02	29.75	30.40					39

10.61 Coffe

Sales

 require the use of the “One-Way ANOVA”

945

960

a. At the 0.05 level of significance, is there evidence of a

59 cents	69 cents	79 cents	89 cents	10.61 The per-store daily customer count (i.e., the mean number
964	953	942	920	of customers in a store in one day) for a nationwide convenience
972					950	937	918	store chain that operates nearly 10,000 stores has been
962	959		945	9												25	steady, at 900, for some time. To increase the customer count,
968	955	948	919	the chain is considering cutting prices for coffee beverages. The
975		960	915	question to be determined is how much to cut prices to increase
954	941	906	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
difference in the daily customer count based on the price
of a small coffee?

11.25

73

75 97

At the 0.05 level of significance, is there evidence of a

52 79 107

95 83 76

Media	Under 36	36-50	50+	11.25 Where people turn for news is different for various
Local TV		107	119	1						33	age groups. A study indicated where different age groups
National TV	102	127	primarily get their news:
Radio	109
Local Newspaper	significant relationship between the age group and where
Internet	people primarily get their news? If so, explain the
relationship.

12.1

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

prediction line:

Yi = 2 + 5Xi

12.4Pet Food

Sales

5

0

5

0

1

5

0

10

0

10

0

10

1

15

0

0

15

0

15

1

20 260 0

20

0

20

1

Shelf Space	Aisle		Location	12.4 The marketing manager of a large supermarket					(assume “Calories” is the “x” variable and “Fat” is the “y” variable)
160	chain has the business objective of using
																																																																		22	shelf space most efficiently. Toward that goal, she would
140	like to use shelf space to predict the sales of pet food. Data
190	is collected from a random sample of 12 equal-sized stores,
240	with the following results
	260
																																										23		a. Construct a scatter plot.
2				70	For these data, and
280	b. Interpret the meaning of the slope, in this problem.
c. Predict the weekly sales of pet food for stores with 8 feet
290	of shelf space for pet food.
310

12.9

Rent

Rent

(assume “Calories” is the “x” variable and “Fat” is the “y” variable)

950

950

in

a. Construct a scatter plot.

700

1650

1400

1450

1100

1200 1150
1150

1600

1650

1200

800

1200

	Size	12.9 An agent for a residential real estate company has the
	850	business objective of developing more accurate estimates of
			1600				1450	the monthly rental cost for apartments. Toward that goal, the
							1200		1085	agent would like to use the size of an apartment, as defined
	1500		1232	by square footage to predict the monthly rental cost. The
	718	agent selects a sample of 25 apartments in a particular residential
1		700		1485	neighborhood and collects the following data (stored
					1650		1136
9				35		726
	875	b. Use the least-squares method to determine the regression
					1150		956	coefficients b0 and b1.
			1400				1100	c. Interpret the meaning of b0 and b1 in this problem.
	1285	d. Predict the monthly rent for an apartment that has 1,000
	2300		1985	square feet.
1		800		1369
	1175
	1225
	1245
		1700		1259
	896
	1361
	1040
	755
	1000
	1750

12.17 Restaurants

Location

21 19 20 60 0 62

(assume “Calories” is the “x” variable and “Fat” is the “y” variable)

City 24 24 20 68 0 67

City 22 14 14 50 0 23
City 27 23 24

0 79

City 20 13 19 52 0 32

City 19 11 18 48 0 38

City 21 23 20 64 0 46

City 19 17 19 55 0 43

City 21 16 19 56 0 39
City 16 15 17 48 0 43
City 20 26 19 65 0 44
City 23 15 17 55 0 29
City 22 23 21 66 0 59
City 21 16 20 57 0 56
City 19 16 18 53 0 32
City 25 22 22 69 0 56
City 22 12 17 51 0 23
City 21 12 16 49 0 40
City 22 19 20 61 0 45
City 17 15 19 51 0 44
City 23 18 21 62 0 40
City 21 17 20 58 0 33
City 23 23 21 67 0 57
City 19 17 17 53 0 43
City 22 16 19 57 0 49
City 21 20 20 61 0 28
City 19 16 16 51 0 35
City 24 20 24 68 0 79
City 19 18 17 54 0 42
City 19 11 12 42 0 21
City 23 16 18 57 0 40
City 19 20 23 62 0 49
City 19 18 18 55 0 45
City 23 20 21 64 0 54
City 25 21 22 68 0 64
City 20 20 17 57 0 48
City 18 14 17 49 0 41
City 24 19 20 63 0 34
City 22 24 21 67 0 53
City 18 15 17 50 0 27
City 22 17 21 60 0 44
City 23 20 22 65 0 58
City 21 19 21 61 0 68
City 22 26 20 68 0 59
City 18 18 18 54 0 61
City 23 17 20 60 0 59
City 22 14 18 54 0 48
City 24 24 25 73 0 78
City 19 21 18 58 0 65
City 20 15 19 54 0 42

22 17 21 60 1 53

Suburban 22 18 21 61 1 45
Suburban 20 13 17 50 1 39
Suburban 21 16 20 57 1 43
Suburban 24 19 20 63 1 44
Suburban 19 16 16 51 1 29
Suburban 22 22 21 65 1 37
Suburban 23 16 20 59 1 34
Suburban 18 19 19 56 1 33
Suburban 18 17 17 52 1 37
Suburban 22 17 22 61 1 54
Suburban 22 17 20 59 1 30
Suburban 19 22 17 58 1 49
Suburban 21 12 19 52 1 44
Suburban 15 20 16 51 1 34
Suburban 22 20 22 64 1 55
Suburban 20 18 18 56 1 48
Suburban 18 16 18 52 1 36
Suburban 22 16 21 59 1 29
Suburban 22 21 23 66 1 40
Suburban 19 19 19 57 1 38
Suburban 24 18 20 62 1 38
Suburban 25 21 24 70 1 55
Suburban 24 21 20 65 1 43
Suburban 20 13 17 50 1 33
Suburban 18 19 18 55 1 44
Suburban 22 15 19 56 1 41
Suburban 18 15 20 53 1 45
Suburban 23 25 21 69 1 41
Suburban 20 22 22 64 1 42
Suburban 20 19 17 56 1 37
Suburban 24 19 22 65 1 56
Suburban 24 27 24 75 1 60
Suburban 21 18 21 60 1 46
Suburban 17 14 18 49 1 31
Suburban 23 15 22 60 1 35
Suburban 24 21 21 66 1 68
Suburban 25 17 22 64 1 40
Suburban 21 19 20 60 1 51
Suburban 23 12 24 59 1 32
Suburban 21 15 19 55 1 28
Suburban 19 19 18 56 1 44
Suburban 26 13 18 57 1 26
Suburban 19 18 20 57 1 42
Suburban 21 11 16 48 1 37
Suburban 27 20 23 70 1 63
Suburban 24 20 20 64 1 37
Suburban 19 11 16 46 1 22
Suburban 23 21 20 64 1 53
Suburban 24 18 22 64 1 62

Food

Décor

Service

Summated Rating

Coded Location

Cost

12.17 In Problem 12.5 on page 441, you used the summated

require the use of the “Regression” function within the Data Analysis menu in Excel

City

rating to predict the cost of a restaurant meal. For those data,

SSR = 6,951.3963 and SST = 15,890.11.

74

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?

Suburban

12.21 Rent

Rent Size

 require the use of the “Regression” function within the Data Analysis menu in Excel

950 850

(assume “Calories” is the “x” variable and “Fat” is the “y” variable)

1600 1450

1200 1085
1500 1232

950 718 its meaning.
1700 1485

1650 1136 c. How useful do you think this regression model is for predicting

726

875 700

1150 956

1400 1100
1650 1285
2300 1985

1369
1400 1175
1450 1225
1100 1245
1700 1259
1200 1150
1150 896
1600 1361
1650 1040
1200 755
800 1000
1750 1200

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 Using the results of that problem,
a. determine the coefficient of determination, and interpret
b. determine the standard error of the estimate.
935	the monthly rent?
d. Can you think of other variables that might explain the
variation in monthly rent?
1800

12.43 Restaurants

Location Food Décor Service Summated Rating Coded Location Cost

 require the use of the “Regression” function within the Data Analysis menu in Excel

City 21 19 20 60 0 62

(assume “Calories” is the “x” variable and “Fat” is the “y” variable)

City 24 24 20 68 0 67

City 22 14 14 50 0 23

City 27 23 24 74 0 79 a. At the 0.05 level of significance, is there evidence of a
City 20 13 19 52 0 32

City 19 11 18 48 0 38

City 21 23 20 64 0 46

City 19 17 19 55 0 43

City 21 16 19 56 0 39
City 16 15 17 48 0 43
City 20 26 19 65 0 44
City 23 15 17 55 0 29
City 22 23 21 66 0 59
City 21 16 20 57 0 56
City 19 16 18 53 0 32
City 25 22 22 69 0 56
City 22 12 17 51 0 23
City 21 12 16 49 0 40
City 22 19 20 61 0 45
City 17 15 19 51 0 44
City 23 18 21 62 0 40
City 21 17 20 58 0 33
City 23 23 21 67 0 57
City 19 17 17 53 0 43
City 22 16 19 57 0 49
City 21 20 20 61 0 28
City 19 16 16 51 0 35
City 24 20 24 68 0 79
City 19 18 17 54 0 42
City 19 11 12 42 0 21
City 23 16 18 57 0 40
City 19 20 23 62 0 49
City 19 18 18 55 0 45
City 23 20 21 64 0 54
City 25 21 22 68 0 64
City 20 20 17 57 0 48
City 18 14 17 49 0 41
City 24 19 20 63 0 34
City 22 24 21 67 0 53
City 18 15 17 50 0 27
City 22 17 21 60 0 44
City 23 20 22 65 0 58
City 21 19 21 61 0 68
City 22 26 20 68 0 59
City 18 18 18 54 0 61
City 23 17 20 60 0 59
City 22 14 18 54 0 48
City 24 24 25 73 0 78
City 19 21 18 58 0 65
City 20 15 19 54 0 42
Suburban 22 17 21 60 1 53
Suburban 22 18 21 61 1 45
Suburban 20 13 17 50 1 39
Suburban 21 16 20 57 1 43
Suburban 24 19 20 63 1 44
Suburban 19 16 16 51 1 29
Suburban 22 22 21 65 1 37
Suburban 23 16 20 59 1 34
Suburban 18 19 19 56 1 33
Suburban 18 17 17 52 1 37
Suburban 22 17 22 61 1 54
Suburban 22 17 20 59 1 30
Suburban 19 22 17 58 1 49
Suburban 21 12 19 52 1 44
Suburban 15 20 16 51 1 34
Suburban 22 20 22 64 1 55
Suburban 20 18 18 56 1 48
Suburban 18 16 18 52 1 36
Suburban 22 16 21 59 1 29
Suburban 22 21 23 66 1 40
Suburban 19 19 19 57 1 38
Suburban 24 18 20 62 1 38
Suburban 25 21 24 70 1 55
Suburban 24 21 20 65 1 43
Suburban 20 13 17 50 1 33
Suburban 18 19 18 55 1 44
Suburban 22 15 19 56 1 41
Suburban 18 15 20 53 1 45
Suburban 23 25 21 69 1 41
Suburban 20 22 22 64 1 42
Suburban 20 19 17 56 1 37
Suburban 24 19 22 65 1 56
Suburban 24 27 24 75 1 60
Suburban 21 18 21 60 1 46
Suburban 17 14 18 49 1 31
Suburban 23 15 22 60 1 35
Suburban 24 21 21 66 1 68
Suburban 25 17 22 64 1 40
Suburban 21 19 20 60 1 51
Suburban 23 12 24 59 1 32
Suburban 21 15 19 55 1 28
Suburban 19 19 18 56 1 44
Suburban 26 13 18 57 1 26
Suburban 19 18 20 57 1 42
Suburban 21 11 16 48 1 37
Suburban 27 20 23 70 1 63
Suburban 24 20 20 64 1 37
Suburban 19 11 16 46 1 22
Suburban 23 21 20 64 1 53
Suburban 24 18 22 64 1 62

12.43 In Problem 12.5 on page 441, you used the summated

rating of a restaurant to predict the cost of a meal.

Using the results of that problem, b1 = 1.2409 and Sb1 b1 = 1.2409 = 0.1421.

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, b1.