Chapter 14, Problem 34SE

How would you rate yourself as a driver? According to a survey conducted by the Field Institute,¹³ most Californians think that they are good drivers but have little respect for the driving ability of others. The data in the following tables show the distribution of opinions, according to gender, for two different questions. Data in the first table give the results obtained when drivers rated themselves; the second table gives the results obtained when drivers rated others. Although not stated in the source, we assume that there were 100 men and 100 women in each of the surveyed groups.

1. a Refer to the table in which drivers rated themselves. Is there sufficient evidence to indicate that there is a difference in the proportions in the three ratings categories for male and female drivers? Give bounds for the p-value associated with the test.
2. b Refer to the table in which drivers rated others. Is there sufficient evidence to indicate that there is a difference in the proportions in the four ratings categories when rating male and female drivers? Give bounds for the p-value associated with the test.
3. c Have you violated any assumptions in your analyses in parts (a) and (b)? What effect might these violations have on the validity of your conclusions?