First, let's calculate the sample mean. The mean is calculated by adding all values and dividing by the number of values:
[tex]\begin{gathered} \bar{x}=\frac{65+71+73+71+71+64}{6}\\ \\ \bar{x}=\frac{415}{6}\\ \\ \bar{x}=69.17 \end{gathered}[/tex]
Now, for the margin of error, we can use the formula below:
[tex]ME=z\cdot\frac{\sigma}{\sqrt{n}}[/tex]
For a 90% interval, we use z = 1.645, so we have:
[tex]\begin{gathered} ME=1.645\cdot\frac{2}{\sqrt{6}}\\ \\ ME=1.343 \end{gathered}[/tex][tex]\begin{gathered} ME=1.645\cdot\frac{2}{\sqrt{6}}\\ \\ ME=1.34 \end{gathered}[/tex]
Then, the confidence interval is given by:
[tex]\begin{gathered} (\bar{x}-ME,\bar{x}+ME)\\ \\ =\\ \\ (67.83,70.51) \end{gathered}[/tex]
