During his presidential campaign, one candidate gave hundreds of speeches in which he mentioned the unemployment rate, promising to fix the “broken”

economy if elected. One reporter noticed that the rates the candidate cited tended to be higher than the official unemployment rate released by the Federal Reserve, 4%. The reporter didn’t have the resources to analyze the hundreds of speeches that the candidate had delivered on the campaign trail, so she collaborated with a political science professor at a nearby university on analyzing a sample of the candidate’s speeches. After drawing a random sample of thirty speeches, they found that the unemployment rate stated by the candidate in the sample was, on average, 12%, with a standard deviation of 2%.

They set up a hypothesis test to calculate the chance that sampling variability explained why this figure was so much higher than the Federal Reserve’s.

a. Which type of hypothesis test should they conduct: a test for a mean or proportion? Explain why.

b. Conduct the appropriate test, with an alpha-level of .05. Is the result of the test statistically significant? Explain why or why not.

c. Based on the results of the test, what is the probability that the sample of the candidate’s speeches is actually indicative of all of his campaign speeches in terms of the difference between the unemployment rates that he cites and the rate given by the Federal Reserve?

d. Do you find the difference between the candidate’s mean cited unemployment rate, 12%, and the one given by the Federal Reserve, 4%, to have practical significance? Explain your answer.