91Ó°ÊÓ

This continues exercise \(3.1 \mathrm{ln} 2005,65 \%\) of the respondents gave medical doc- tors a rating of "very high or high," compared to a 67\(\%\) rating for druggists. Is the difference real, or a chance variation? Or do you need more information to decide? If the difference is real, how would you explain it? Discuss briefly. You may assume that the results are based on a simple random sample of \(1,000\) persons taken in \(2005 ;\) each respondent rated clergy, medical doctors, druggists, and many other professions.

An investigator wants to show that first-born children score higher on IQ tests than second-borns. He takes a simple random sample of 400 two-child families in a school district, both children being enrolled in elementary school. He gives these children the WISC vocabulary test (described in exercise 7 on pp. \(507-508\) ) with the following results. \(\cdot\) The 400 first-borns average 29 and their \(S D\) is 10 . \(\cdot\) The 400 second-borns average 28 and their \(S D\) is 10 . (Scores are corrected for age differences.) He makes a two-sample z-test: SE for first-born average \(\approx 0.5\) SE for second-born average \(\approx 0.5\) SE for difference \(=\sqrt{0.5^{2}+0.5^{2}} \approx 0.7\) \(z=1 / 0.7 \approx 1.4, \quad P \approx 8 \%\) Comment briefly on the use of statistical tests.