A Gallup survey of 1001 randomly selected U.S. adults conducted May 2011 asked, “In your opinion, which one of the following is the main reason why students get education beyond high school?” Fifty-three percent chose “to earn more money.” Based on these data, we found the 95% confidence interval for the proportion of U.S. adults who choose “to earn more money” to be (0.499, 0.561). Suppose that the sample size was 2,002 instead, while the proportion of respondents choosing “to earn more money” was still 53%.
a. True or false? A 95% confidence interval based on these altered data would be narrower, because a larger sample size increases confidence, which in turn makes the interval narrower.
b. True or false? A 95% confidence interval based on these altered data would be narrower, because a larger sample size decreases the variability of the statistic.
c. True or false? A 95% confidence interval based on these altered data would be wider, because a larger sample size increases confidence, which in turn makes the interval wider.

d. True or false? A 95% confidence interval based on these altered data would be wider, because a larger sample size increases the variability of the statistic.