On January 30, 1995, Time magazine reported the results of a poll of adult Americans, in which they were asked, “Have you ever driven a car when you probably had too much alcohol to drive safely?” The exact results were not given, but from the information provided we can guess at what they were. Of the 300 men who answered, 189 (63%) said yes and 108 (36%) said no. The remaining three weren’t sure. Of the 300 women, 87 (29%) said yes while 210 (70%) said no, and the remaining three weren’t sure.
a. Ignoring those who said they weren’t sure, there were 297 men asked, and 189 said yes, they had driven a car when they probably had too much alcohol. Does this provide statistically significant evidence that a majority of men in the population (that is, more than half) would say that they had driven a car when they probably had too much alcohol, if asked? Go through the four steps to test this hypothesis.
b. For the test in part (a), you were instructed to perform a one- sided test. Why do you think it would make sense to do so in this situation? If you do not think it made sense, explain why not.
c. Repeat parts (a) and (b) for the women. (Note that of the 297 women who answered, 87 said yes.)
The following information is for Exercises 20 to 22: In Example 23.3 (p. 501), we tested to see whether dieters and exercisers had significantly different average fat loss. We concluded that they did because the difference for the samples under consideration was 1.8 kg, with a standard error of 0.83 kg and a standardized score of 2.17. Fat loss was higher for the dieters.