Introduction to Probability and Statistics for Engineers and Scientists

474 Chapter 10:Analysis of Variance

9. The following data relate to the ages at death of a certain species of rats that were
   fed 1 of 3 types of diet. Thirty rats of a type having a short life span were randomly
   divided into 3 groups of size 10 each. The sample means and sample variances of
   the ages at death (measured in months) of the 3 groups are as follows:

Very Low Calorie Moderate Calorie High Calorie

Sample mean 22.4 16.8 13.7

Sample variance 24.0 23.2 17.1

Test the hypothesis, at the 5 percent level of significance, that the mean lifetime

of a rat is not affected by its diet. What about at the 1 percent level?

10.Plasma bradykininogen levels are related to the body’s ability to resist inflamma-

tion. In a 1968 study (Eilam, N., Johnson, P. K., Johnson, N. L., and Creger, W.,

“Bradykininogen levels in Hodgkin’s disease,”Cancer, 22 , pp. 631–634), levels

were measured in normal patients, in patients with active Hodgkin’s disease, and

in patients with inactive Hodgkin’s disease. The following data (in micrograms of

bradykininogen per milliliter of plasma) resulted.

Normal Active Hodgkin’s Disease Inactive Hodgkin’s Disease

5.37 3.96 5.37

5.80 3.04 10.60

4.70 5.28 5.02

5.70 3.40 14.30

3.40 4.10 9.90

8.60 3.61 4.27

7.48 6.16 5.75

5.77 3.22 5.03

7.15 7.48 5.74

6.49 3.87 7.85

4.09 4.27 6.82

5.94 4.05 7.90

6.38 2.40 8.36

Test, at the 5 percent level of significance, the hypothesis that the mean

bradykininogen levels are the same for all three groups.

11.A study of the trunk flexor muscle strength of 75 girls aged 3 to 7 was reported

by Baldauf, K., Swenson, D., Medeiros, J., and Radtka, S., “Clinical assessment

of trunk flexor muscle strength in healthy girls 3 to 7,”Physical Therapy, 64 , pp.

1203–1208, 1984. With muscle strength graded on a scale of 0 to 5, and with 15

girls in each age group, the following sample means and sample standard deviations

resulted.