The table shows the number satisfied in their work in a sample of working adults

Question

The table shows the number satisfied in their work in a sample of working adults with a college education and in a sample of working adults without a college education. Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p_1 > p_2. Find the critical value(s) for this hypothesis test (to nearest thousandth). Do the data provide sufficient evidence that a greater proportion of those with a college education are satisfied in their work? A. z = plusminus 1.960; no B. z = -1.645; yes C. z = 1.960; yes D. z = 1.645; no

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 = 0.319

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

SE = 0.0535

z = (p1 - p2) / SE

z = 0.626

zcritical = 1.645

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 more than 0.626. We use the Normal Distribution Calculator to find P(z > 0.626) = 0.2643

Interpret results. Since the P-value (0.2643) 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 a greater proportion of those with a college education are satisfied in their work.

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