In Example 13.2, we revisited data from Case Study 6.3, regarding testing to see if there was a relationship between gender and driving after drinking. We found that we could not rule out chance as an explanation for the sample data; the chi- square statistic was 1.637, and the p-value was 0.20. Now suppose that the sample contained three times as many drivers, but the proportions of males and females who drank before driving were still 16% and 11.6%, respectively.
a. What would be the value of the chi- square statistic for this hypothetical larger sample?
b. The p-value for the test based on the larger sample would be about 0.03. Restate the hypotheses being tested and explain which one you would choose on the basis of this larger hypothetical sample.
c. In both the original test and the hypothetical one based on the larger sample, the probability of making a type 1 error if there really is no relationship is 5%. Assuming there is a relationship in the population, would the power of the test— that is, the probability of correctly finding the relationship—be higher, lower, or the same for the sample three times larger compared with the original sample size?