Question

This is AP Statistics Question. Can you help me with this?

Answer 1

The confidence interval is given by


`\mu_s\pm Z_(\alpha_0)\sigma_s`

where
`\mu_s` is the sample mean and
`\sigma_s` is the standard error of the mean. In turn, the standard error of the mean is
`\sigma_s=\frac\sigma{\sqrt n}` where
`n` is sample size.

We have


`\sigma_s=\frac6{√(25)}=1.2`

The endpoints of the confidence interval correspond to the finite endpoints of the rejection region. That is,


`\begin{cases}\mu_s-1.2Z_(\alpha_0)=28\\\mu_s+1.2Z_(\alpha_0)=32\end{cases}`

for which we can solve for
`Z_(\alpha_0)`. We get


`Z_(\alpha_0)=\frac53\approx1.67`

which is the critical value for a confidence level of
`\alpha_0\approx90.44\%`.