Stock market traders anxiously wait for the federal government's release of the August numbers for nonfarm payrolls - the whisper number according to financial analysts. Last year month of August showed an average of 50,000 new jobs with a standard deviation of 20,000. A sample of 100 nonfarm payrolls taken earlier in the week shows a sample mean of 55,000. Conduct a hypothesis test to determine whether the whisper number justifies a conclusion of a statistically significant change in the number of new jobs with respect to last year. Allow for 10% error in the test. The hypothesis setting for the test follows.

H_{0 :} =50,000

H_a : 50,000

Conduct a hypothesis test using a critical-value approach

Conduct a hypothesis test using a p-value approach.

According to the statistical analysis you have performed above, do you think the whisper number does justify a conclusion of a statistically significant change in the number of new jobs? WHY?