Bluman A.G. Elementary Statistics- A Step By Step Approach

506 Chapter 9 Testing the Difference Between Two Means, Two Proportions, and Two Variancesof less than 80%. At a 0.05, test the claim that there is no difference in theproportions of the small and large nursing homes with a resident vaccination rateof less than 80%.Source: Nancy Arden, Arnold S. Monto, and Suzanne E. Ohmit, “Vaccine Use and the Risk of Outbreaks in a Sample of NursingHomes During an Influenza Epidemic,” American Journal of Public Health.SolutionLet pˆ1 be the proportion of the small nursing homes with a vaccination rate of less than80% and pˆ2 be the proportion of the large nursing homes with a vaccination rate of lessthan 80%. ThenNow, follow the steps in hypothesis testing.Step 1pˆ 1 X 1n 1 1234 0.35 and pˆ 2 X 2n 2 1724 0.71p X 1 X 2 12 17n 1 n 2 34 24 2958 0.5q 1 p 1 0.5 0.5State the hypotheses and identify the claim.H 0 : p 1 p 2 (claim) and H 1 : p 1 p 2Step 2 Find the critical values. Since a 0.05, the critical values are 1.96and 1.96.Step 3Compute the test value.z pˆ 1 pˆ 2 p 1 p 2 A p q ¢ 1 n 1 1 n 2≤0.35 0.71 0A 0.50.5 ¢ 134 1 0.360.1333 2.724 ≤Step 4Make the decision. Reject the null hypothesis, since 2.7 1.96.See Figure 9–8.Figure 9–8Critical and Test Valuesfor Example 9–9–2.7 –1.960+1.96Step 5Summarize the results. There is enough evidence to reject the claim that thereis no difference in the proportions of small and large nursing homes with aresident vaccination rate of less than 80%.9–36