Identify the null hypothesis, Ho, and the alternative hypothesis, Ha. Determine
ID: 3063708 • Letter: I
Question
Identify the null hypothesis, Ho, and the alternative hypothesis, Ha. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Find the critical value(s) and identify the rejection region(s). Find the appropriate standardized test statistic. If convenient, use technology. Decide whether to reject or fail to reject the null hypothesis. Interpret the decision in the context of the original claim. In a random sample of 1276 U.S. adults, 903 favor using mandatory testing to assess how well schools are educating students. In another random sample of 1112 U.S. adults taken 9 years ago, 799 favored using mandatory testing to assess how well schools are educating students. At = 0.05, can you support the claim that the proportion of U.S. adults who favor mandatory testing to assess how well schools are educating students is less than it was 9 years ago
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1> P2
Alternative hypothesis: P1 < P2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.7127
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.01855
z = (p1 - p2) / SE
z = - 0.58
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than - 0.58
Thus, the P-value = 0.281
Interpret results. Since the P-value (0.281) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the claim that the proportion of U.S. adults who favor mandatory testing to assess how well schools are educating students is less than it was 9 years ago.