Chapter 9.2, Problem 25BB

Pooling Repeat Exercise 12 “IQ and Lead” by assuming that the two population standard deviations are equal, so σ₁ = σ₂. Use the appropriate method from Part 2 of this section. Does pooling the standard deviations yield results showing greater significance?

12. IQ and Load Exposure Data Set 7 “IQ and Lead” in Appendix B lists full IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The statistics are summarized below.

a. Use a 0.05 significance level to test the claim that the mean IQ score of people with low blood lead levels is higher than the mean IQ score of people with high blood lead levels.

b. Construct a confidence interval appropriate for the hypothesis test in part (a).

c. Does exposure to lead appear to have an effect on IQ scores?

Low Blood Lead Level: n = 78, $\bar{x}$ = 92.88462, s = 15.34451

High Blood Lead Level: n = 21, $\bar{x}$ = 86.90476, s = 8.988352