8.31 The Wilson estimate for the high tech companies is 0.7957 offering stock options. For non-high tech, the Wilson estimate is 0.6847. The difference is 0.1110 with a SE of 0.0608. The 95% interval for the mean difference (high tech – non-high tech) is from 0.0081 to 0.2301.

8.33 The Wilson estimate for complainers who leave is 0.0858. For non-complainers, the estimate is 0.0309. The difference is 0.0549 with a SE of 0.01275. The 95% interval is from 0.0299 to 0.0799.

8.34 H₀: p₁ = p₂ vs. H_a: p₁ > p₂, where p₁ refers to the complainers and p₂ refers to the non-complainers. The pooled estimate is 0.055 and the SE is 0.0123. The Z statistic is 4.463, which is extremely significant. This is extremely strong evidence that complainers have a higher probability of leaving than the non-complainers.

8.41 (a) Test H₀: p₁ = p₂ vs. H_a: p₁ ¹ p₂, where Population 1 is rural and Population 2 is Urban. (b) The pooled estimate of p is 0.36342, with a SE of 0.0483. Z=1.222 and the p-value is 0.22. This is not significant. (c) The difference in Wilson estimators is 0.059 with SE=0.0484. The 95% interval is -0.036 to +0.154.