# HW8 - HW8(MWF ppl due M 11/19 TTh ppl due Tu 11/20...

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HW8 (MWF ppl – due M, 11/19; TTh ppl – due Tu, 11/20) Name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .UMID . . . . . . . . . . . . . . . . . . . . . . . Lecture: MWF TTh GSI: Carrie Katherine Lin Lab Section # . About a proportion: Suppose 20% of U.S. adults have a vitamin B deficiency. a. That 20% is a parameter, right? However, as a researcher, you’re unaware of that 20%, so you take a sample of size 100 and determine X = the # of adults with a vitamin B deficiency. Here, the expected value of X = . . . . . . . . . whereas the std dev of X = . . . . . . . . . . b. In your experiment, suppose x = 27 so that p ˆ = 0.27 (or 27%). That 27% is a . . . . . . . . . . . . . . Consider all possible p ˆ s from a sample of size 100. Then the mean (or expected value) of all of those p ˆ s = . . . . . . ., whereas the standard deviation of all of those p ˆ s = . . . . . . . . . And the shape of that distribution of those p ˆ s is . . . . . . . . . . . . . . . . . c. But your p ˆ is 0.27. If p = 0.20, how unlikely is an estimate of 0.27? Said in another way, what is the probability of a p ˆ (n=100) that is 0.27 or greater? Hint: Use the distribution on p519 in the book. P( p ˆ 0.27) = . . . . . . . . d. Does the answer for P( p ˆ 0.27) seem to make p ˆ =0.27 (or more extreme) UNLIKELY?

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