You are investigating the diﬀerence in blood sugar between female and male monkeys when they are both given a high carbohydrate diet for a week. Each monkey in the study is to be matched with another monkey of opposite sex, of similar age, and size. From similar studies done in the past, it is known that female monkeys, on average, increase 10 more milligrams per decilitre than male monkeys do post-diet. These studies also indicate that the standard deviation of their diﬀerence in blood sugar post-diet is 3 milligrams per decilitre. Suppose it is reasonable to assume that the diﬀerence in blood sugar between male and female monkeys post-diet is normally distributed. Fifteen female and ﬁfteen male monkeys have just ﬁnished going through this experiment, and their average diﬀerence in blood sugar is to be measured.
(A-1) What is the correct notation for the statistic of interest?
(A-2) What is the mean of the sampling distribution of the sample mean diﬀerence in blood sugar between the female and the male monkeys post-diet?
(A-3) What is the standard deviation of the sampling distribution of the sample mean diﬀerence in blood sugar between the female and male monkeys?
(A-4) What is the probability that the diﬀerence between average blood sugar increase of the male monkeys in the sample and the blood sugar increase of the female monkeys is less than 8 milligrams per decilitre?
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