Consider the following three relative frequency histograms. Each histogram was constructed by selecting 100 random samples from a population composed of 40% women and 60% men. For each sample, the sample proportion of women, ˆ p , was computed and the 100 ˆ p values were used to construct the histogram. For each histogram, a different sample size was used. One histogram was constructed using 100 samples of size 20, one was constructed using 100 samples of size 40, and one was constructed using 100 samples of size 100.

a. These three histograms are approximate sampling distributions of ˆ p for the three different sample sizes. Which histogram corresponds to the sample size that would produce sample proportions that varied the most from sample to sample?
b. Match the three sample sizes to the three histograms. That is, which histogram is the approximate sampling distribution for sample size 5 20, which is for sample size 5 40, and which is for sample size 5 100? Explain how you made your choices.

Histogram I Relative frequency 0.40 0.30 0.20 0.10 0.0 0.2 0.3 0.4 Sample proportion 0.5 0.6 Histogram II Relative frequency 0.40- 0.30- 0.20 0.10 0.3 0.4 Sample proportion 0.2 0.5 0.6 Histogram IIl Relative frequency 0.40 0.30 0.20 0.10- 0,0 0.2 0.3 0.4 0.5 0.6 Sample proportion