In the United States, the population mean height for 10-year-old girls is 54.5 inches. Suppose a random sample of 15 10-year-old girls from Brazil is taken and that these girls had a sample mean height of 53.2 inches with a standard deviation of 2.5 inches. Assume that heights are Normally distributed.

a. Determine whether the population mean for height for 10-year-old girls from Brazil is significantly different from the U.S. population mean. Use a significance level of 0.05.

b. Now suppose the sample consists of 40 girls instead of 15. Repeat the test.

c. Explain why the t-values and p-value for parts a and b are different.