Exercise 7.5 We are planning an experiment on the quality of video tape and have purchased 24 tapes, four tapes from each of six types. The six types of tape were 1) brand Ahigh cost, 2) brand A low cost, 3) brand B high cost, 4) brand B low cost, 5) brand C high cost, 6) brand D high cost. Each tape will be recorded with a series of standard test patterns, replayed 10 times, and then replayed an eleventh time into a device that measures the distortion on the tape. The distortion measure is the response, and the tapes will be recorded and replayed in random order. Previous similar tests had an error variance of about .25. a) What is the power when testing at the .01 level if the high cost tapes have an average one unit different from the low cost tapes? b) How large should the sample size have been to have a 95% brand A versus brand B condence interval of no wider than 2? Problem 7.1 We are interested in the effects of soy additives to diets on the blood concentration of estradiol in premenopausal women. We have historical data on six subjects, each of whose estradiol concentration was measured at the same stage of the menstrual cycle over two consecutive cycles. On the log scale, the error variance is about .109. In our experiment, we will have a pretreatment measurement, followed by a treatment, followed by a post-treatment measurement. Our response is the difference (post - pre), so the variance of our response should be about .218. Half the women will receive the soy treatment, and the other half will receive a control treatment. How large should the sample size be if we want power .9 when testing at the . 05 level for the alternative that the soy treatment raises the estradiol concentration 25% (about . 22 log units)? Problem 7.2: Non-digestible carbohydrates can be used in diet foods, but they may have effects on colonic hydrogen production in humans. We want to test to see if inulin, fructooligosaccharide, and lactulose are equivalent in their hydrogen production. Preliminary data suggest that the treatment means could be about 45, 32, and 60 respectively, with the error variance conservatively estimated at 35. How many subjects do we need to have power .95 for this situation when testing at the E1 = .01 level