Question: IQ test scores. Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:
(a) We expect the distribution of IQ scores to be close to Normal. Make a histogram of the distribution of these 31 scores. Does your plot show outliers, clear skewness, or other non-Normal features? Using a calculator, find the mean and standard deviation of these scores.
(b) Treat the 31 girls as an SRS of all middle-school girls in the school district. Give a 95% confidence interval for the mean score in the population.
(c) In fact, the scores are those of all seventh-grade girls in one of the several schools in the district. Explain carefully why we cannot trust the confidence interval from (b).