Chapter 7, Problem 81SE

Gender and Use of Turn Signals Statistics student Hector Porath wanted to find out whether gender and the use of turn signals when driving were independent. He made notes when driving in his truck for several weeks. He noted the gender of each person that he observed and whether he or she used the turn signal when turning or changing lanes. (In his state, the law says that you must use your turn signal when changing lanes, as well as when turning.) The data he collected are shown in the table.

a. What percentage of men used turn signals, and what percentage of women used them?

b. Assuming the conditions are met (although admittedly this was not a random selection), find a $95\%$ confidence interval for the difference in percentages. State whether the interval captures 0, and explain whether this provides evidence that the proportions of men and women who use turn signals differ in the population.

c. Another student collected similar data with a smaller sample size:

First find the percentage of men and the percentage of women who used turn signals, and then, assuming the conditions are met, find a $95\%$ confidence interval for the difference in percentages. State whether the interval captures 0, and explain whether this provides evidence that the percentage of men who use turn signals differs from the percentage of women who do so.

d. Are the conclusions in parts b and c different? Explain.