Do the data provide sufficient evidence that a greater proportion of those with a college education are satisfied in their work?

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 p1>p2. Find the critical value(s) for this hypothesis test.

College Education No college education

Number in sample 194 188

number satisfied in their work 74 70

A)z=1.645;no

B)z=-1.645;yes

C)z=1,96;yes

D)z=+-1.96;no

Answer 1

Since we are testing a claim about two population proportions with a right-tailed hypothesis test at the α = 0.05 significance level and the test statistic that corresponds to our hypothesis test has a standard normal distribution, the critical value is z = 1.645. Since the test statistic is z = 0.18 and is less than the critical value we conclude that the data do not provide sufficient evidence that a greater proportion of those with a college education are satisfied in their work. All of this tells us that the correct answer is A.