QUESTION 1 Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized, double-blind, placebo-controlled experiment was carried out to compare olestra potato chips to regular potato chips with respect to GI symptoms ("Gastrointestinal Symptoms Following Consumption of Olestra or Regular Triglyceride Potato Chips," J. of the Amer. Med. Assoc., 1998: 150-152). A researcher believes that the percentage of GI symptoms among all people who eat Olestra chips is higher than the percentage of GI symptoms among all people who eat regular chips. Test the researcher's claim at a = 0.01. Set up HO and Ha. O HO: H1- H2 20 Ha: H1-H2 0 where 1 = average number of GI symptoms among people who eat Olestra chips and M2 = average number of GI symptoms among people who eat regular chips O HO: p1 - p2 50 Ha: pl - p2 > 0 where pl = percentage of GI symptoms among people who eat Olestra chips and p2 = percentage of GI symptoms among people who eat regular chipsQUESTION 2 #1 continued. Let p1 = percentage of GI symptoms among people who eat Olestra chips and p2 = percentage of GI symptoms among people who eat regular chips. What are type I error and type II error? 0 Type I error: the researcher concludes that on average there are more cases of GI symptoms among people who eat Olestra chips than among people who eat regular chips when actually it is false. Type II error: the researcher concludes that on average there are more cases of GI symptoms among people who eat regular chip than among people who eat Olestra chips when actually it is false. 0 Type I error: the researcher concludes that p1 is higher than p2 when actually p1 is less than or equal to p2. Type II error: the researcher concludes that pl is less than or equal to p2 when actually pl is higher than pl. 0 Type I error: the researcher concludes that p1 is less than or equal to p2 when actually p1 is higher than p2. Type II error: the researcher concludes that pl is higher than p2 when actually pl is less than or equal to p2. 0 Type I error: the researcher concludes that on average there are more cases of GI symptoms among people who eat regular chip than among people who eat Olestra chips when actually it is false. Type II error: the researcher concludes that on average there are more cases of GI symptoms among people who eat Olestra chips than among people who eat regular chips when actually it is false. QUESTION 3 The Edison Electric Institute has published figures on the number of kilowatt hours used annually by various home appliances. It is claimed that a vacuum cleaner uses an average of 46 kilowatt hours per year. If a random sample 12 homes included in a planned study indicates that vacuum cleaners use an average of 42 kilowatt hours per year with a standard deviation of 11.9 kilowatt hours, does this suggest at 0.05 level of significance that vacuum cleaners use, on average, less than 46 kilowatt hours annually? Assume the population of kilowatt hours to be normal. Set up HO and Ha. O HO: H 46 O HO: H > 46 Ha: M S 46QUESTION 4 #3 continued. What are type I and type H error? 0 Type I error: it is concluded that the number of kilowatt hours used by vacuum cleaners is 46 kilowatt hours annually when actually it is different from 46 kilowatt hours. Type 11 error: it is concluded that the number of kilowatt hours used by vacuum cleaners is 46 kilowatt hours annually when actually it is different from 46 kilowatt hours. 0 Type I error: it is concluded that vacuum cleaners use on average at least 46 kilowatt hours annually when actually they use less than 46 kilowatt hours on average. Type 11 error; it is concluded that vacuum cleaners use on average less than 46 kilowatt hours annually when actually they use at least 46 kilowatt hours on average. 0 Type I error: it is concluded that the number of kilowatt hours used by vacuum cleaners is different from 46 kilowatt hours annually when actually it is 46 kilowatt hours. Type 11 error: it is concluded that the number of kilowatt hours used by vacuum cleaners is 46 kilowatt hours annually when actually it is different from 46 kilowatt hours. 0 Type I error: it is concluded that vacuum cleaners use on average less than 46 kilowatt hours annually when actually they use at least 46 kilowatt hours on average. Type 11 error: it is concluded that vacuum cleaners use on average at least 46 kilowatt hours annually when actually they use less than 46 kilowatt hours on average