Introduction to Probability and Statistics for Engineers and Scientists

Problems 475

Age 34567

Sample mean 3.3 3.7 4.1 4.4 4.8

Sample standard deviation .9 1.1 1.1 .9 .5

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

flexor strength is the same for all five age groups.

12.An emergency room physician wanted to know whether there were any differences

in the amount of time it takes for three different inhaled steroids to clear a mild

asthmatic attack. Over a period of weeks she randomly administered these steroids

to asthma sufferers, and noted the time it took for the patients’ lungs to become

clear. Afterward, she discovered that 12 patients had been treated with each type

of steroid, with the following sample means (in minutes) and sample variances

resulting.

Steroid Xi S^2 i

A 32 145

B 40 138

C 30 150

(a) Test the hypothesis that the mean time to clear a mild asthmatic attack is the

same for all three steroids. Use the 5 percent level of significance.

(b) Find confidence intervals for all quantitiesμi−μjthat, with 95 percent

confidence, are valid.

13.Five servings each of three different brands of processed meat were tested for fat

content. The following data (in fat percentage per gram) resulted.

Brand 1 2 3

32 41 36

Fat 34 32 37

content 31 33 30

35 29 28

33 35 33

(a) Does the fat content differ depending on the brand?

(b) Find confidence intervals for all quantitiesμi−μjthat, with 95 percent

confidence, are valid.

14.A nutritionist randomly divided 15 bicyclists into 3 groups of 5 each. The first

group was given a vitamin supplement to take with each of their meals during the