Introduction to Probability and Statistics for Engineers and Scientists

512 Chapter 11:Goodness of Fit Tests and Categorical Data Analysis

Determine the p-value of the test that a family’s income and region are

independent.

16.The following data relate the mother’s age and the birthweight (in grams) of her

child.

Birthweight

Maternal Age Less Than 2,500 Grams More Than 2,500 Grams

20 years or less 10 40

Greater than 20 15 135

Test the hypothesis that the baby’s birthweight is independent of the mother’s age.

17.Repeat Problem 16 with all of the data values doubled — that is, with these data:

20 80

30 270

18.The number of infant mortalities as a function of the baby’s birthweight (in grams)

for 72,730 live white births in New York in 1974 is as follows:

Outcome at the End of 1 Year

Birthweight Alive Dead

Less than 2,500 4,597 618

Greater than 2,500 67,093 422

Test the hypothesis that the birthweight is independent of whether or not the baby

survives its first year.

19.An experiment designed to study the relationship between hypertension and

cigarette smoking yielded the following data.

Nonsmoker Moderate Smoker Heavy Smoker

Hypertension 20 38 28

No hypertension 50 27 18

Test the hypothesis that whether or not an individual has hypertension is

independent of how much that person smokes.

20.The following table shows the number of defective, acceptable, and superior items

in samples taken both before and after the introduction of a modification in the

manufacturing process.