Introduction to Probability and Statistics for Engineers and Scientists

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

Test the hypothesis that the percentages of the surgical operations that lead to

lawsuits are the same for each of the three types.

(a) Use the 5 percent level of significance.

(b) Use the 1 percent level of significance.

24.In a famous article (S. Russell, “A red sky at night...,”Metropolitan Magazine

London, 61 , p. 15, 1926) the following data set of frequencies of sunset colors and

whether each was followed by rain was presented.

Sky Color Number of Observations Number Followed by Rain

Red 61 26

Mainly red 194 52

Yellow 159 81

Mainly yellow 188 86

Red and yellow 194 52

Gray 302 167

Test the hypothesis that whether it rains tomorrow is independent of the color of

today’s sunset.

25.Data are said to be from alognormaldistribution with parametersμandσif the

natural logarithms of the data are normally distributed with meanμand standard

deviationσ. Use the Kolmogorov–Smirnov test with significance level .05 to

decide whether the following lifetimes (in days) of a sample of cancer-bearing

mice that have been treated with a certain cancer therapy might come from a

lognormal distribution with parametersμ=3 andσ=4.

24, 12, 36, 40, 16, 10, 12, 30, 38, 14, 22, 18