## Elementary Statistics (12th Edition)

$\alpha=1-0.95=0.05.$ $\sigma$ is unknown, hence we use the t-distribution with $df=sample \ size-1=7-1=6$ in the table. $t_{\alpha/2}=t_{0.025}=2.447.$ Margin of error:$t_{\alpha/2}\cdot\frac{\sigma}{\sqrt {n}}=2.447\cdot\frac{5.6}{\sqrt{7}}=5.2.$ Hence the confidence interval:$\mu$ is between 42.7-5.2=37.5 and 42.7+5.2=47.9. We are 95% confident that the mean chest declaration measurement is between 37.5 and 47.9.