Use the applet Confidence Intervals for a Mean (the impact of not knowing the standard deviation) to compare proportions of z-intervals and t-intervals that contain the mean for a population that is normally distributed.

a. Using n = 5 and the normal distribution with mean 50 and standard deviation 10, run the applet several times.

How do the proportions of z-intervals and t-intervals that contain the mean compare?

b. Repeat part a first for n = 10 and then for n = 20.

Compare your results with those in part a.

c. Describe any patterns you observe between the proportion of z-intervals that contain the mean and the proportion of t-intervals that contain the mean as the sample size increases.