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Sample proportion for samples of size 70 Histogram A 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 p was calculated The 100 p values were used to construct the histogram Histogram B was constructed in a similar way but using samples of size 70 a Which of the two histograms indicates that the value of p has smaller sample to sample variability How can you tell Histogram A indicates that the value of p has smaller sample to sample variability than Histogram B because Histogram A has values that tend to deviate more from the center than Histogram B indicating a larger standard deviation of the values of p O Histogram A indicates that the value of p has smaller sample to sample variability than Histogram B because Histogram A has values that tend to deviate less from the center than Histogram B indicating a larger standard deviation of the values of p Histogram B indicates that the value of p has smaller sample to sample variability than Histogram A because Histogram B has values that tend to deviate more from the center than Histogram A indicating a larger standard deviation of the values of p Histogram B indicates that the value of p has smaller sample to sample variability than Histogram A because Histogram B has values that tend to deviate less from the center than Histogram A indicating a smaller standard deviation of the values of p Histogram A indicates that the value of p has smaller sample to sample variability than Histogram B because Histogram A has values that tend to deviate less from the center than Histogram B indicating a smaller standard deviation of the values of p b For which of the two sample sizes n 40 or n 70 do you think the value of p would be less likely to be close to 0 20 What about the given histograms supports your choice Samples of size n 70 would yield a value of p that is less likely to be close to 0 20 because the histogram for n 70 seems to have less sample to sample variability Samples of size n 40 would yield a value of p that is less likely to be close to 0 20 because the histogram for n 40 seems to have more sample to sample variability Samples of size n 40 would yield a value of p that is less likely to be close to 0 20 because the histogram for n 40 seems to have less sample to sample variability O Samples of size n 70 would yield a value of p that is less likely to be close to 0 20 because the histogram for n 70 seems to have more sample to sample variability O Samples of size n 40 would yield a value of p that is less likely to be close to 0 20 because the histogram for n 40 is not centered at 0 20

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