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stat512prob2 - 6 Calculate power for the slope using the...

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Statistics 512: Problem Set No. 2 Due Friday, September 17th, 2010 (4:30pm) The next 5 problems continue the analysis of the plastic hardness data begun in the first homework. 1. Plot the data using proc gplot . Include a smoothed function on the plot by using the i = smnn option on the symbol1 statement, where nn is a number between 1 and 99. Is the relationship approximately linear? 2. Plot the 95% bounds (confidence band) for the mean (use i=rlclm on the symbol1 statement). 3. Plot the 95% bounds for individual observations (using i=rlcli ). 4. Give an estimate of the mean hardness that you would expect after 36 and 43 hours; and a 95% confidence interval for each estimate. Which confidence interval is wider and why is it wider? 5. Give a prediction for the hardness that you would expect for an individual piece of plastic after 43 hours; give a 95% prediction interval for this quantity.
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Unformatted text preview: 6. Calculate power for the slope using the results of text Problem 1.22 as follows. Assume n = 16, σ 2 = MSE , and SS X = 1280. (Note: this last value could be obtained with SAS using proc univariate data = (dataset name); var time; and looking at the output titled “ Corrected SS ” in the Moments section.) (a) Find the power for rejecting the null hypothesis that the regression slope is zero using an α = 0 . 05 significance test when the alternative is β 1 = 0 . 5. (b) Plot the power as a function of β 1 for values of β 1 between -2.5 and +2.5 in increments of 0.25 . 7. Given that R 2 = SSM/SST , it can be shown that R 2 / (1-R 2 ) = SSM/SSE . If you have n = 28 cases and R 2 = 0 . 3, what is the F-statistic for the test that the slope is equal to zero? 1...
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