Chapter 9, Problem 43SE

Male Height In the United States, the population mean height for 3-year-old boys is 38 inches $\left(\text{http://www}\text{.kidsgrowth}\text{.com}\right)$. Suppose a random sample of 15 non-U.S. 3-year-old boys showed a sample mean of $37.2$ inches with a standard deviation of 3 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population.

a. Determine whether the population mean for non-U.S. boys is significantly different from the U.S. population mean. Use a significance level of $0.05$.

b. Now suppose the sample consists of 30 boys instead of 15, and repeat the test.

c. Explain why the $t\text{-values}$ and $\text{p-values}$ for parts a and b are different.