Following are the data on percentage of investments in energy securities and tax efficiency from Exercise 14.16.

a. Obtain a point estimate for the mean tax efficiency of all mutual fund portfolios with 6% of their investments in energy securities.
b. Determine a 95% confidence interval for the mean tax efficiency of all mutual fund portfolios with 6% of their investments in energy securities.
c. Find the predicted tax efficiency of a mutual fund portfolio with 6% of its investments in energy securities.
d. Determine a 95% prediction interval for the tax efficiency of a mutual fund portfolio with 6% of its investments in energy securities.
e. Draw graphs similar to those in Fig. 14.11 on page 574, showing both the 95% confidence interval from part (b) and the 95% prediction interval from part (d).
f. Why is the prediction interval wider than the confidence interval?
Presuming that the assumptions for regression inferences are met, determine the required confidence and prediction intervals.

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x 3.1 3.2 3.7 4.3 4.0 5.5 6.7 7.4 74 10.6 y| 98.1 94.7 92.0 89.8 87.5 85.0 82.0 77.8 72.1 53.5