Use the applet Confidence Intervals for a Proportion to investigate the effect of the value of p on the number of confidence intervals that contain the population proportion p for a fixed sample size. For this exercise, use sample size n = 10.

a. Run the applet several times without clearing for p = .1. What proportion of the 95% confidence intervals contain p? What proportion of the 99% confidence intervals contain p? Do the results surprise you?

Explain.

b. Repeat part a for each value of p: p = .2, p = .3, p = .4, p = .5, p = .6, p = .7, p = .8, and p = .9.

c. Which value of p yields the greatest proportion of each type of interval that contain p?

d. Based on your results, what values of p will yield more reliable confidence intervals for a fixed sample size n?

Explain.