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Chapter 7: Problem 65
For a population, \(N=12,000\) and \(p=.71\). A random sample of 900 elements selected from this population gave \(\hat{p}=.66 .\) Find the sampling error.
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How does the value of \(\sigma_{\bar{x}}\) change as the sample size increases? Explain.
For a population, \(N=30,000\) and \(p=.59 .\) Find the \(z\) value for each of the following for \(n=100\). a. \(\hat{p}=.56\) \(\begin{array}{lll}\text { b. } \hat{p}=.68 & \text { c. } \hat{p}=.53 & \text { d. } \hat{p}=.65\end{array}\)
A Census Bureau report revealed that \(43.7 \%\) of Americans who moved between 2009 and 2010 did so for housing-related reasons, such as the desire to live in a new or better home or apartment (http://www.census.gov/newsroom/releases/archives/mobility_of_the_population/cb11-91.html). Suppose that this percentage is true for the current population of Americans. a. Suppose that \(49 \%\) of the people in a random sample of 100 Americans who moved recently did so for housing-related reasons. How likely is it for the sample proportion in a sample of 100 to be \(.49\) or more when the population proportion is \(.437 ?\) b. Refer to part a. How likely is it for the sample proportion in a random sample of 200 to be 49 or more when the population proportion is .437? c. What is the smallest sample size that will produce a sample proportion of \(.49\) or more in no more than \(5 \%\) of all sample surveys of that size?
For a population, \(N=10,000, \mu=124\), and \(\sigma=18 .\) Find the \(z\) value for each of the following for \(n=36\) a. \(\bar{x}=128.60 \quad\) b. \(\bar{x}=119.30 \quad\) c. \(\bar{x}=116.88 \quad\) d. \(\bar{x}=132.05\)
A population has a normal distribution. A sample of size \(n\) is selected from this population. Describe the shape of the sampling distribution of the sample mean for each of the following cases. a. \(n=23\) b. \(n=450\)
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