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Americans on Marriage: Statistical Insights from a Sample
Chapter 5, Problem 17(choose chapter or problem)
According to a study done by the Pew Research Center, 39% of adult Americans believe that marriage is now obsolete.
(a) Suppose a random sample of 500 adult Americans is asked whether marriage is obsolete. Describe the sampling distribution of \(\hat{p}\), the proportion of adult Americans who believe marriage is obsolete.
(b) What is the probability that in a random sample of 500 adult Americans less than 38% believe that marriage is obsolete?
(c) What is the probability that in a random sample of 500 adult Americans between 40% and 45% believe that marriage is obsolete?
(d) Would it be unusual for a random sample of 500 adult Americans to result in 210 or more who believe marriage is obsolete?
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QUESTION:
According to a study done by the Pew Research Center, 39% of adult Americans believe that marriage is now obsolete.
(a) Suppose a random sample of 500 adult Americans is asked whether marriage is obsolete. Describe the sampling distribution of \(\hat{p}\), the proportion of adult Americans who believe marriage is obsolete.
(b) What is the probability that in a random sample of 500 adult Americans less than 38% believe that marriage is obsolete?
(c) What is the probability that in a random sample of 500 adult Americans between 40% and 45% believe that marriage is obsolete?
(d) Would it be unusual for a random sample of 500 adult Americans to result in 210 or more who believe marriage is obsolete?
ANSWER:Step 1 of 4
(a) Suppose a random sample of 500 adult Americans is asked whether marriage is obsolete. The sampling distribution of \(\widehat{p}\) , the proportion of adult Americans who believe marriage is obsolete is
The sampling distribution of \(\widehat{p}\) is approximately normal with
\(\mu_{\hat{p}}=\frac{39}{100}=0.39 \text { and } \sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{(0.39)(1-0.39)}{500}}=0.0218\)
If n \(\leq\) 0.05N, then the shape of the distribution is approximately normal as long as
np(1 - p) \(\geq\) 10.
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Americans on Marriage: Statistical Insights from a Sample
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Review a Pew Research Center study on Americans' beliefs about marriage. Through statistical analysis, understand the sampling distribution, standard deviation, and the probabilities surrounding various beliefs. The insights detail public sentiments and the significance of sample outcomes.
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