## Elementary Statistics (12th Edition)

$\alpha=1-0.9=0.1.$ $\sigma$ is unknown, hence we use the t-distribution with $df=sample \ size-1=40-1=39$ in the table. $t_{\alpha/2}=t_{0.05}=1.685.$ Margin of error:$t_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=1.685\cdot\frac{2.28}{\sqrt{40}}=0.61.$ Hence the confidence interval:$\mu$ is between 7.15-0.61=6.54 and 7.15+0.61=7.76. This cannot be generalized to men, because the data is only based on women.