Use this worksheet to study the effect of sample size on the shape of the sampling distribution with µ = 24 and sigma = 2. Purple shaded area represents P(x_a ≤ X ≤ x_b). As you adjust the sample size n, note how the standard error of the mean changes, and thus how the shape of the sampling distribution changes.

How does the probability P(23 < x-bar < 25) change as n increases? Does it increase or decrease? How does the probability P(26 < x-bar < 27) change as n increases? Does it increase or decrease? Thinking about sample size and sample means, will large samples have greater variability or less variability in sample means than small samples ?