Question 21.34

21.34 IQ test scores. Here are the IQ test scores of 31 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 93

  1. (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.

  2. (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.

  3. (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).