The US Census indicates that 35% of US residents are less than 25 years old. Figure 3.7 shows possible sampling distributions for the proportion of a sample less than 25 years old, for samples of size n = 20, n = 100, and n = 500.

Figure 3.7

(a) Which distribution goes with which sample size?
(b) If we use a proportion p̂, based on a sample of size n = 20, to estimate the population parameter p = 0.35, would it be very surprising to get an estimate that is off by more than 0.10 (that is, the sample proportion is less than 0.25 or greater than 0.45)? How about with a sample of size n = 100? How about with a sample of size n = 500?
(c) Repeat part (b) if we ask about the sample proportion being off by just 0.05 or more.
(d) Using parts (b) and (c), comment on the effect that sample size has on the accuracy of an estimate.

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