IQ scores are desinged to be normally distributed with standard deviation 15. Below are the IQ scores of a random sample of 30 seventh grade girls in a Midwest school district.
114, 100, 104, 89, 102, 91, 114, 114, 103, 105, 108, 130, 120, 132, 111, 128, 118, 119, 86, 72, 111, 103, 74, 112, 107, 103, 98, 96, 112, 112
Find a 90% confidence lower bound for the mean IQ score of girls in this school district.
Okay, so I think I want to go after $\overline{X}$ here? For the lower confidence bound, I have $L_C=\overline{X}-q_\alpha\hat{\sigma}_\overline{X}.$
For $\overline{X}$, I have $106.27$. Now for $\hat{\sigma}$ I think the formula should be $\sqrt{\sigma^2/n}$, which is $\sqrt{15^2/30}$ or about $2.74$. But I don't know how to find $q_\alpha$. Any suggestions?
