15.23 The data in the table below first appeared in Exercise 4.11.

The variables are height (short or not) and whether or not the student had ever been bullied in school for 209 secondary school students in England. The researchers gathered the data to test their hypothesis that short students are more likely to be bullied in school than are other students.

Height and Bullying in School Ever Bullied Height Yes No Total Short 42 50 92 Not Short 30 87 117 Total 72 137 209

a. Should these data be analyzed by using a chi-square test or a z-test for comparing two proportions? Explain.

b. Explain why it makes sense to designate height as the explanatory variable.

c. Carry out an appropriate hypothesis test. Be sure to state null and alternative hypotheses, and clearly indicate your conclusion about these hypotheses.