Suppose that, unbeknownst to you, \( 60 \% \) of the students at your large school typically ride the bus to school. You and a friend are taking random samples of students to estimate this proportion. You take a sample of 30 students and your friend takes a sample of 60 students. Would it be more surprising to have a sample proportion of 0.70 for you or your friend?
A sample proportion of 0.70 would be equally surprising, since you are both estimating the same proportion.
A sample proportion of 0.70 would be more surprising for you, since there is more variability in sample proportions with larger sample sizes.
A sample proportion of 0.70 would be more surprising for your friend, since there is less variability in sample proportions with larger sample sizes.
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