12.73 Exercise 4.11 described a case–control study comparing short to not-short English secondary school students. Of n 5 92 short students, 42 said they had been bullied in school. Of n 5 117 not-short students, 30 said they had been bullied in school. Here is Minitab output for comparing two proportions:

Sample Bullied N Sample p Short 42 92 0.456522 Not Short 30 117 0.256410 Estimate for p(1) 2 p(2): 0.200111 95% lower bound for p(1) 2 p(2): 0.0919200 Test for p(1) 2 p(2) 5 0 (vs . 0): Z 5 3.02 P-Value 5 0.001

a. The researchers wanted to know whether short students are bullied more often. Write the null and alternative hypotheses for this question, defining and using appropriate notation.

b. Use the Minitab output to carry out the remaining steps of the hypothesis test. Use a 5 .05.

c. The Minitab procedure found a one-sided 95% confidence interval for the difference in the two proportions, and the lower end of the interval is given in the output.

What is the upper end of the interval? Write the complete interval.

d. Use the one-sided 95% confidence interval to test the hypotheses stated in part (a).

Section 12.4 Skillbuilder Exercises