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

Section 8–4 z Test for a Proportion 439Figure 8–26Critical and Test Valuesfor Example 8–17–1.96 0 1.15 +1.96Step 5Summarize the results. There is not enough evidence to reject the claim that60% of people are trying to avoid trans fats in their diets.Example 8–18Family and Medical Leave ActThe Family and Medical Leave Act provides job protection and unpaid time off fromwork for a serious illness or birth of a child. In 2000, 60% of the respondents of asurvey stated that it was very easy to get time off for these circumstances. A researcherwishes to see if the percentage who said that it was very easy to get time off haschanged. A sample of 100 people who used the leave said that 53% found it easy to usethe leave. At a 0.01, has the percentage changed?Source: Department of Labor.SolutionStep 1 State the hypotheses and identify the claim.H 0 : p 0.60 and H 1 : p 0.60 (claim)Step 2 Find the critical value(s). Since a 0.01 and this test is two-tailed, thecritical values are 2.58.Step 3 Compute the test value. It is not necessary to find pˆ since it is given in theexercise; pˆ 53%. Substitute in the formula and evaluate.p 0.6 and q 1 p 1 0.6 0.4z pˆ p 0.53 0.60pqn 0.60.4100 1.43Step 4Make the decision. Do not reject the null hypothesis, since the test value fallsin the noncritical region, as shown in Figure 8–27.Figure 8–27Critical and Test Valuesfor Example 8–18–2.58 –1.430+2.58Step 5Summarize the results. There is not enough evidence to support the claim thatthe percentage of those using the medical leave said that it was easy to get haschanged.8–41