Exercises - Hypothesis Tests for Proportions (Two Samples)

  1. In Cleveland, a sample of 73 mail carriers showed that 10 had been bitten by an animal during one week. In Philadelphia, in a sample of 80 mail carriers, 16 had received animal bites. Is there a significant difference in the proportions? Use the confidence interval method with $\alpha = 0.05$.

  2. Chantix is a drug used as an aid to stop smoking. The numbers of subjects experiencing insomnia for each of two treatment groups in a clinical trial of the drug Chantix are given below. Use the P-value method with a significance level of 0.05 to test the claim that there is more insomnia in the treatment group. $$\begin{array}{l|r|r} & \textrm{Chantix Treatment} & \textrm{Placebo}\\\hline \textrm{Number in Group} & 129 & 805\\\hline \textrm{Number Experiencing Insomnia} & 19 & 13\\\hline \end{array}$$

  3. A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were killed. Construct a 90% confidence interval estimate of the difference between the fatality rates for those not wearing seat belts and those wearing seat belts. What does the result suggest about the effectiveness of seat belts?