Consider the two relative frequency histograms at the bottom of this page. The histogram on the left was constructed by selecting 100 different random samples of size 50 from a population consisting of 55% females and 45% males. For each sample, the sample proportion of females, ˆ p , was computed. The 100 ˆ p values were used to construct the histogram. The histogram on the right was constructed in a similar way, except that the samples were of size 75 instead of 50.

a. Which of the two histograms shows more sample- to-sample variability? How can you tell?
b. For which of the two sample sizes, n = 50 or n = 75, do you think the value of ˆ p is more likely to be close to 0.55? What about the given histograms supports your choice?

HISTOGRAMS FOR EXERCISE 8.2 Relative frequency 0.25 0.20- 0.15 0.10 0.5 0.0 040 45 0.50 055 060 0.65 0.70 Sample proponion