A Wall Street Journal poll asked 35 economic forecasters to predict the interest rate on 3-month Treasury bills 12 months later [9]. These 35 forecasts had a mean of 6.19 and a variance of 0.47. Assuming these to be a random sample, give a 95 percent confidence interval for the mean prediction of all economic forecasters and explain why each of these interpretations is or is not correct:

a. There is a 0.95 probability that the actual Treasury bill rate is in this interval.

b. Approximately 95 percent of the predictions of all economic forecasters are in this interval.