We want a 95% 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, 10 get the correct answer.

a. Using software or the Sampling Distributions applet on the text CD, set the population menu to Binary and treat the sample proportion as the population proportion by setting the proportion parameter to 0.20 = 10/50 (Binary: p = 0.2). Take a random sample of size 50, and find the sample proportion of correct answers.

b. Take 100 resample’s like the one in part a, each time calculating the sample proportion. Take one sample at a time, recording each sample proportion. Now, construct a 90% confidence interval by identifying the 5th and 95th percentiles of the sample proportions. This is the 90% bootstrap confidence interval.

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