In the United States, the population mean height for 3-year-old boys is 38 inches (www.kidsgrowth.com). 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-values and p-values for parts a and b are different.