Qusetion: Your broker achieved a rate of return of 18.3% on your portfolio last year. For a sample of 25 other brokers in the area, according to a recent news article, the average rate of return was 15.2% with a standard deviation of 3.2% (as percentage points).
a. To test whether your broker significantly outperformed this group, identify the idealized population and the hypotheses being tested. In particular, are you testing against a mean or against a new observation?
b. Find the standard error for prediction.
c. Find the two-sided 95% prediction interval for a new observation.
d. Did your broker outperform this group?
e. Did your broker significantly outperform this group?
f. Find the t-value and the p-value (as either p > 0.05, p < 0.05, p < 0.01, p < 0.001) sided test.