Chapter 9, Problem 44SE

Female Height 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. $\left(\text{Source: cdc}\text{.gov}\right)$

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 $t\text{-values}$ and $\text{p-value}$ for parts a and b are different.