A student working on a history project decided to find a 95 percent confidence interval for the difference in mean age at the time of election to office for former American Presidents versus former British Prime Ministers. The student found the ages at the time of election to office for the members of both groups, which included all of the American Presidents and all of the British Prime Ministers, and used a calculator to find the 95 percent confidence interval based on the t-distribution. This procedure is not appropriate in this context because
the sample sizes for the two groups are not equal.

a. the entire population was measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.
b. elections to office take place at different intervals in the two countries, so the distribution of ages cannot be the same.
c. ages at the time of election to office are likely to be skewed rather than bell-shaped, so the assumptions for using this confidence interval formula are not valid.
d. sages at the time of election to office are likely to have a few large outliers, so the assumptions for using this confidence interval formula are not valid.