Checkpoint: \"Distribution of Sample Proportions\" Question 1 Single adults: Acc

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Checkpoint: "Distribution of Sample Proportions" Question 1 Single adults: According to a Pew Research Center analysis of census data, Select all that apply in 2012, 20% of American adults ages 25 and older had never been married. | 10 points Suppose that we select random samples from this population of American adults ages 25 and older. For each sample we then calculate the proportion that had never been married. For which of the following sample sizes will the sampling distribution be approximately normal? Wang, W., and Parker, K. (2014). Record Share of Americans Have Never Been Married. Pew Research Center, http://www.pewsocialtrends.org/2014/09/24/record-share-of-americans-have- never-married/ A. 25 B. 50 C. 75 Question 2

Explanation / Answer

For this we use Central limit theorem, it says that the sampling distribution of sample mean is approximately normal regardless of the shape of the population. So the sampling size may be n>=30. Here there is 20% polpulation exists above the 25 and with 25 who had never married. So the sampling distribution will be approximately normal for the sample sizes 50 or 75. To get perfect distribution we can choose 75. So here option B and C exists.

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