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.
The 400 first-borns average 29 and their SD is 10
The 400 second-borns average 28 and their SD is 10.
(Scores are corrected for age differences) He makes a two-sample z-test:
SE for the first-born average=0.5
SE for the second-born average=0.5
SE for difference = square root of (0.5^2+0.5^2)=0.7 z=1/0.7=1.4, p=8%
Comment briefly on the use of statistical tests.