Use the applet Confidence Intervals for a Proportion to investigate the effect of the sample size on the number of confidence intervals that contain the population proportion p for a value of p close to 0 or 1.

a. Run the applet several times without clearing for p = .5 and n = 50. Record the proportion of the 99% confidence intervals containing p.

b. Now set p = .1 and run the applet several times without clearing for n = 50. How does the proportion of the 99% confidence intervals containing p compare with that in part a?

c. Repeat part b, keeping p = .1 and increasing the sample size by 50 until you find a sample size that yields a similar proportion of the 99% confidence intervals containing p as that in part a.

d. Based on your results, describe how the value of p affects the sample size needed to guarantee a certain level of confidence.