The mean height of American males is 69.5 inches. The heights of the 43 male U.S. presidents* (Washington through Obama) have a mean 70.78 inches and a standard deviation of 2.77 inches. Treating the 43 presidents as a simple random sample, determine if there is evidence to suggest that U.S. presidents are taller than the average American male. Use the \(\alpha=0.05\) level of significance.

Approach Assume that all U.S. presidents come from a population whose height is 69.5 inches (that is, there is no difference between heights of U.S. presidents and the general American male population). Then determine the likelihood of obtaining a sample mean of 70.78 inches or higher from a population whose mean is 69.5 inches.
If the result is unlikely, reject the assumption stated in the null hypothesis in favor of the more likely notion that the mean height of U.S. presidents is greater than 69.5 inches. However, if obtaining a sample mean of 70.78 inches from a population whose mean is assumed to be 69.5 inches is not unusual, do not reject the null hypothesis (and attribute the difference to sampling error). Assume the population of potential U.S. presidents is large (for independence). Because the sample size is large, the distribution of \(\bar{x}\) is approximately normal. Follow Steps 1 through 5.