Statistical Inference: Confidence Intervals and Hypothesis Tests. Suppose that a sample of economists are forecasting whether and by how much the Federal Reserve Bank will change the federal funds rate when they meet in early February. Of the 20 economists surveyed, 5 believe that the Fed will leave the federal funds rate unchanged at 2.00%, 4 believe that the Fed will raise the rate to 2.25%, and 11 believe that the Fed will cut the rate to 1.75%.
a. Find the mean and standard deviation for the forecasted federal funds rate in this sample of economists.
b. Using the calculations from part a, and the methods described in class, find out a 99 percent confidence interval for the population mean forecast, where the population 3 would consist of all economists. [Hint: Be sure to use the standard error, not the standard deviation only, in your calculation.]
c. What assumptions are needed to justify the methods used in parts a and b?
d. What if you were told that all economists in the sample were employed at UC campuses? Which of the assumptions given in c do you think would be violated?