Use the applet entitled Confidence Intervals for a Mean (the impact of confidence level) to investigate the effect of the sample size on the proportion of confidence intervals that contain the mean when the underlying distribution is skewed. Set the distribution to right skewed, the mean to 10, and the standard deviation to 1.
a. Using n = 30, run the applet several times without clearing. What happens to the proportion of 95% confidence intervals that contain the mean as you run the applet more and more? What happens to the proportion of 99% confidence intervals that contain the mean as you run the applet more and more? Do the proportions seem to be approaching the values that you would expect?
b. Clear and run the applet several times, using n = 100. What happens to the proportions of 95% confidence intervals and 99% confidence intervals that contain the mean this time? How do these results compare with your results in part a?
c. Clear and run the applet several times, using n = 1000. How do the results compare with your results in parts a and b?
d. Describe the effect of sample size on the likelihood that a confidence interval contains the mean for a skewed distribution.
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