Inference and Sampling Distributions

 Practice Problems

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1. If you wanted to estimate the range of heights of people in a 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 inches?

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
randomly selected sapling will be less than 1.7 inches tall? If yes, compute that probability. If not, explain why not.

Check your solutions.