Analysis of Variance

1. In a completely randomized experimental design, three brands of paper towels were

tested for their ability to absorb water. Equal size towels were used, with four

selections of towels tested per brand. The absorbency rating data follow. At a .05 level

of significance, does there appear to be a difference in the ability of the brands to

absorb water?

Brand

X Y Z

91 99 83

100 96 88

88 94 89

89 99 76

Answer: Significant; p value = .0134

2. Money magazine reports percentage returns and expense ratios for stock and bond

funds. The following data are the expense ratios for 10 midcap stock funds, 10 small

cap stock funds. 10 hybrid stock funds, and 10 specialty stock funds (Money, March

2003)

Midcap Small cap Hybrid Specialty

1.2 2.0 2.0 1.6

1.1 1.2 2.7 2.7

1.0 1.7 1.8 2.6

1.2 1.8 1.5 2.5

1.3 1.5 2.5 1.9

1.8 2.3 1.0 1.5

1.4 1.9 0.9 1.6

1.4 1.3 1.9 2.7

1.0 1.2 1.4 2.2

1.4 1.3 0.3 0.7

Use = .05 to test for any significance difference in the mean expense ratio among the

four types of stock funds.

Answer: Significant; p Value = .046

3. Three difference assembly methods have been proposed for a new product. A

completely randomized experimental design was chosen to determine which assembly

method results in the greatest number of parts produced per hour, and 30 workers

were randomly selected and assigned to use one of the purposed methods. The

number of units produced by each worker follows.

Method

A B C

97 93 99

73 100 94

93 93 87

100 55 66

73 77 59

91 91 75

100 85 84

86 73 72

92 90 88

95 83 86

Answer: Not Significant; p Value = .2455

Multiple Regressions

1. The personnel director for Electronics Associates developed the following estimated

regression equation relating an employees score on a job satisfaction test to his or her

length of service and wage rate.

21 5.1369.84.14 xxy

Where,

x1= length of service (years)

X2 = wage rate (dollars)

Y = job satisfaction test score (higher scores indicate greater job

satisfaction)

a. Interpret the coefficients in this estimated regression equation.

b. Develop an estimate of the job satisfaction test for an employee who has four years of

service and makes $6.50 per hour. Answer: 67.39

2. Recall that in exercise 49, the admissions officer for Clearwater College developed the

following estimated regression equation relating final collage GPA to the students SAT

mathematics score and high school GPA.

21 00486.0235.41.1 xxy

Where,

X1 = high school grade point average

X2 = SAT mathematics score

Y = final college grade point average

a. Complete the missing entries in this output. Answer:

21 00486.0235.41.1 xxy

b. Compute F and test at a .05 level of significance to see whether a significance

relationship is present. Answer: Significant ; p Value = .0001

c. Did the estimated regression equation provide a good fit to the data? Explain.

Answer: R2 = .937; Ra2 = 9.19; good fit

d. Use the t test and = .05 to test H0: 1 = 0 and H0 : 2 = 0.Answer: Both

significant

3. Recall that in exercise 50 the personnel director for Electronic Associates developed

the following estimated regression equation relating an employees score on a job

satisfaction test to length of service and wage rate.

21 5.1369.84.14 xxy

Where,

X1 = length of service (years)

X2 = wage rate (dollars)

Y = job satisfaction test scores (higher scores indicated greater job satisfaction)

a. Complete the missing entries in this output.

b. Compute F and test using = .05 to see whether a significant relationship is present.

c. Did the estimated regression equation provide a good fit to the data? Explain.

d. Use the t test and = .05 to test H0: 1 = 0 and H0: 2 = 0.

4. Smart Money magazine evaluated 65 metropolitan areas to determine where home

values are headed. An ideal city would get a score of 100 if all factors measured were as

favorable as possible. Areas with a score of 60 or greater are considered to be primed

for price appreciation, and areas with a score of below 50 may see housing value erode.

Two of the factors evaluated were the recession resistance of the area and its

affordability. Both of these factors were rated using a scale ranging from 0 (low score) to

10 (high score). The data obtained for a sample of 20 cities evaluated by SmartMoney

follow (Smart Money, February 2002).

a. Develop an estimated regression equation that can be used to predict the score

given the recession resistance rating. At the .05 level of significance, test for a

significant relationship. Answer: Score = 50.6 + 1.56 RecRes

b. Did the estimated regression equation developed in part (a) provide a good fit to the

data? Explain. Answer: r2 = .431; not a good fit

c. Develop an estimated regression equation that can be used to predict the score

given the recession resistance rating and the affordability rating. At the .05 level of

significance, test for overall significance. Answer: Score = 33.5 + 1.90 RecRes +2.61

Afford Significant , Ra2 = .784; much better fit