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, 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 first-born average: 0.5
SE for 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.