Question

As of August 2018, the unemployment rate for Americans whose maximum attained level of education is a high school diploma is 3.9%. Is the unemployment rate significantly different for Americans who have earned their bachelors degrees? Suppose we have a random sample of 500 Americans whose maximum attained level of education is a bachelor's degree and found 13 who are unemployed. Use these sample results to conduct a hypothesis test to determine whether the unemployment rate for Americans whose maximum attained level of education is a bachelors degree differs significantly from the unemployment rate for Americans whose maximum attained level of education is a high school diploma.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.039
Alternative Hypothesis, Ha: p ≠ 0.039

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.026 - 0.039)/sqrt(0.039*(1-0.039)/500)
z = -1.5

P-value Approach
P-value = 0.1336
As P-value >= 0.05, fail to reject null hypothesis.