Question

Solve the problem.

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 α = 0.05 to test the claim that Find the critical value(s) for this hypothesis test.

Answer 1

The critical values of the hypothesis test is Z = 1.645

Using α = 0.05 ; for a one tailed test where the null and Alternative hypothesis are defined as ;

• 
  `H_(0) : p_(1) < p_(2)`
• 
  `H_(1) : p_(1) > p_(2)`

A one-tailed test, also known as a directional or one-sided test, is a type of hypothesis testing used to determine whether there is a statistically significant on only one side.

A one-tailed test has its critical region only on one side. This reflects the direction specified in the alternative hypothesis. For a one-tailed right test, the critical region lies in the right tail of the distribution, and for a one-tailed left test, it lies in the left tail.

Here, the alternative hypothesis is ">" hence, our critical region would be to the right and hence, positive.

Now we have ;

α = 0.05

The Zscore at P(z > 0.05) = 1.645

Hence, the critical values for the hypothesis test is Z = 1.645