Statement of a problem № m41278


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?

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