Question: 8.62 Bootstrap interval for the proportion We want a 90% confidence interval for the population proportion of students in a high school in Dallas, Texas,

8.62 Bootstrap interval for the proportion We want a 90%

confidence interval for the population proportion of students in a high school in Dallas, Texas, who can correctly find Iraq on an unlabeled globe. For a random sample of size 50, 5 get the correct answer.

a. Access the Sampling Distribution of the Sample Proportion web app from the book’s website and set the population proportion to p = 0.1, pretending that the population proportion is equal to the sample proportion 110>50 = 0.12. Generate one random sample of size n = 50 and find the sample proportion of correct answers.

b. Take 1,000 resamples like the one in part a (just click the 1,000 option) and find the 5th and 95th percentiles of the simulated sampling distribution. (Note: Click Find Percentile to find the percentiles.) This is the 90%

bootstrap confidence interval for p.

c. Explain why the sample proportion does not fall exactly in the middle of the bootstrap confidence interval. (Hint:

Is the sampling distribution symmetric or skewed?)

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