## Elementary Statistics (12th Edition)

$\alpha=1-0.95=0.05.$ $\sigma$ is not known, hence we use the t-distribution with $df=sample \ size-1=40-1=49$ in the table. $t_{\alpha/2}=t_{0.025}=2.023.$ Margin of error:$t_{\alpha/2}\cdot\frac{s}{\sqrt {n}}=2.023\cdot\frac{5.8}{\sqrt{40}}=1.86.$ Hence the confidence interval:$\mu$ is between 5.5-1.86=3.64 and 5.5+1.86=7.36.