STAT 410 96-2 Assignment 2: Hints

• 2.3: Remember: V(X) is an expected value: E((X-mu)^2) which you find by computing each possible value and multiplying by the correspoding probability. Remeber also that when sampling with replacement there is only one way to get two 8's -- get an 8 on the first draw and an 8 on the second but to get the sample {3,8} there are two ways -- the 8 could be first or it could be second.
• 2.4: Technically the question asks about a confidence level of an interval of the form ybar plus or minus 10% of Ybar. You have to see how many SE's wide such an interval would be, guessing that Ybar and ybar are not too different. Many statisticians would object to the language used by Cochran; this is not really a probability in the classical sense.
• 2.12: To do the first part of this question you have to choose two sample sizes. The variance formula for a difference gives you one equation to solve for two unknowns; you must add on your own the condition that the total sample size be as small as possible. In part b in a sample of size n roughly 0.75n will be owners; you use this with the variance formula to find n.
• 2.13: This question and others use the following formula: E(Y) = sum of E(Y|X=x) times P(X=x) For this question the random variable X is the number of distinct units in the sample.
• 2.15: This question is cancelled. It is probably intended to be done using the material on page 38.
• 2.19: See my hint for question 2.13.

DUE: Friday, 24 May
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