Question

The mean hourly wage for employees in goods-producing industries is currently $24.57. Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries. Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value. Conduct a hypothesis test to determine if the mean hourly wage of employees in the manufacturing industry differs from there ported mean of $24.57 at a level of significance, ?=0.01.

a. Set up the appropriate null and alternative hypotheses.

b. Sketch the rejection region indicating the critical value and the appropriate shaded area.

c. Compute the test statistic and find the p-value.

d. State your conclusion to the hypothesis test using both the critical value and p-value approach.(Be sure to explain the reasoning for your conclusion and state the meaning of your conclusion in terms of the hypotheses and the context of the application of the problem).

(i). Critical value approach

(ii). P-value approach

Answer 1