You wish to test the following claim (H_a) at a significance level of alpha = 0.

Question

You wish to test the following claim (H_a) at a significance level of alpha = 0.05. H_0: P_1 = P_2 H_a: P_1 notequalto P_2 You obtain 48.5% successes in a sample of size n_1 = 549 from the first population. You obtain 45.9% successes in a sample of size n_2 = 444 from the second population. For this test, you should NOT use the continuity connection, and you should use the normal distribution as an approximation for the binomial distribution. What is the test statistic for this sample? test statistic = What is the p-value for this sample? p-value =

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 two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

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 = 0.4734

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

SE = 0.03187

z = (p1 - p2) / SE

z = 0.816

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 two-tailed test, the P-value is the probability that the z-score is less than - 0.82 or greater than 0.82.

Thus, the P-value = 0.2073 + 0.2073 = 0.4146

Interpret results. Since the P-value (0.4146) is greater than the significance level (0.05), we have to accept the null hypothesis.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.