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# ANOVA & Regression Analysis

1. A sporting goods manufacturing company wanted to compare the distance traveled by golf balls produced using each of four different designs. Ten balls were manufactured with each design and were brought to the local golf course for the club professional to test. The order in which the balls were hit with the same club from the first tee was randomized so that the pro did not know which type of ball was being hit. All 40 balls were hit in a short period of time, which the environmental conditions were essentially the same. The results (distance traveled in yards) for the four designs are provided in the following table:
Design
1 2 3 4
206.32 217.08 226.77 230.55
207.94 221.43 224.79 227.95
206.19 218.04 229.75 231.84
204.45 224.13 228.51 224.87
209.65 211.82 221.44 229.49
203.81 213.90 223.85 231.10
206.75 221.28 223.97 221.53
205.68 229.43 234.30 235.45
204.49 213.54 219.50 228.35
210.86 214.51 233.00 225.09

a. At the 0.05 level of significance, is there evidence of difference in the mean distance traveled by the golf balls with a different design?

b. If the results in (a) indicate that it is appropriate, use the Tukey-Kramer procedure to determine which designs differ in mean distance.

c. At he 0.05 level of significance, is there evidence of a difference in the variation of the distance traveled by the golf balls with different designs.

d. What golf ball design should the manufacturing manager choose? Explain.

2. Management of a soft-drink bottling company has the business objective
of developing a method for allocating delivery costs to customers. Although
one cost clearly relates to travel time within a particular route, another
variable cost reflects the time required to unload the cases of soft drink at
the delivery point. To begin decided to develop a regression model to predict
delivery time based on the number of cases delivered. A sample of 20 deliveries
within a territory was selected. The delivery times and the number of cases delivered
were organized in the following table:

Customer Number of Cases Delivery Time (Min)
1 52 32.1
2 64 34.8
3 73 36.2
4 85 37.8
5 95 37.8
6 103 39.7
7 116 38.5
8 121 41.9
9 143 44.2
10 157 47.1
11 161 43.0
12 184 49.4
13 202 57.2
14 218 56.8
15 243 60.6
16 254 61.2
17 267 58.2
18 275 63.1
19 287 65.6
20 298 67.3

a. Use the least squares method to compute the regression coefficients b0 and b1

b.Interprete the meaning of b0 and b1 in this problem

c. Predict the delivery time for 150 cases of soft drink.

d. Should you use the model to predict the delivery time for a customer who is receiving 500 cases
of soft drink? Why or why not?

e. Determine the coefficient of determination, r2, and explain it's meaning in the problem.
f. Perform a residual analysis. Is there any evidence of a pattern in the residuals? Explain.

g. At 0.05 level of significance, is there evidence of a linear relationship between delivery time and the number of cases delivered?

h. Construct a 95% confidence interval estimate of the mean delivery time for 150 cases of soft drink, and a 95% prediction interval of the delivery time for a single delivery of 150 cases of soft drink.

#### Solution Summary

The solution provides step by step method for the calculation of ANOVA, Tukey-Kramer procedure, Levine's test for homogeneity of variance and regression analysis. Formula for the calculation and Interpretations of the results are also included.

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