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 40 from a population consisting of 20% part- time students and 80% full- time students. For each sample, the sample proportion of part- time students, ˆp was computed. The 100 ˆ values were used to construct the histogram. The histogram on the right was constructed in a similar way, but using samples of size 70.
a. Which of the two histograms indicates that the value of ˆ has smaller sample- to- sample variability? How can you tell?
b. For which of the two sample sizes, n = 40 or n = 70, do you think the value of ˆ p would be less likely to be close to 0.20? What about the given histograms supports your choice?