Consider the two relative frequency histograms at the top of the next page. The histogram on the left was constructed by selecting 100 different random samples of size 35 from a population in which 17% donated to a nonprofit organization. For each sample, the sample pro-portion ˆ p was computed and then the 100 ˆ p values were used to construct the histogram. The histogram on the right was constructed in a similar way but used samples of size 110.

a. Which of the two histograms indicates that the value of ˆ p has more sample- to- sample variability? How can you tell?
b. For which of the two sample sizes, n = 35 or n = 110, do you think the value of ˆ p would be more likely to be close to the actual population proportion of p = 0.17? What about the given histograms supports your choice?

Transcribed Image Text:

Relative frequency 0.20 0.15 0.10- 0.5- 0.0 0.10 015 0.20 020.30 035 Sample proportion Relative freauencv 0.25 0.20- 0.15 0.10 0.5 0.0 그 0.30 0.05-·^^0.10 ,0.15, .020, .10.25 Sample proportion