9.5.9. Complete the proof of Theorem 9.5.2.
9.5.10. Construct an 80% confidence interval for the difference PM - pw in the nightmare frequency data summarized in Case Study 9.4.2.
9.5.IL If px and p y denote the true success probabilities associated with two sets of n and m
independent Bernoulli trials, respectively, the ratio
- - - - (px - py )
J (X/n)(l - X /n ) + ( Y/m)(l - Y/ m)
has approximatel y a standard normal distribution. Use that fact to prove Theorem 9.5.3.
9.5.12. Suicide rates in the United States tend to be much higher for men than for women, at all ages. That pattern may not extend to all professions, though. Death certifica tes obtained for the 3637 members of the American Chemical Society who died over a 20-year period revealed that 106 of the 3522 male deaths were suicides, as compared to 13 of the 115 female deaths (103). Construct a 95% confidence interval for the difference in suicide rates. What would you conclude?
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