Unit 9: Sampling Distributions
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You'll need a pencil and paper for these. You can check your
answers with the key offered at the bottom of the page.
1. If you wanted to estimate the range of heights of people in
population (tallest height minus shortest height) you might decide to
take a sample of five people and use the sample range. Would this be an
unbiased estimator of the population range? Explain.
2. Suppose that 29% of all high-school seniors are regular
smokers. (This is approximately true, according to a 2004 Gallup
poll.) If you were take a random sample of 100 high school seniors,
what would be the approximate distribution of the sample proportion of
regular smokers among them?
3. Suppose that the heights of three-month-old red oak
saplings in a greenhouse have a mean of 2.1 inches and a standard
deviation of 1.9 inches. You plan to randomly sample 45 of these
saplings and average their heights together to get x-bar. What is the
probability that the mean of the sample heights will be less than 1.7
4. Again given the supposition that the heights of
three-month-old red oak saplings in a greenhouse have a mean of 2.1
inches and a standard deviation of 1.9 inches, can you calculate the
probability that one