Question

A news article estimated that only 5% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05. (a) A random sample of n = 100 people will be selected from this population and p?, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p?? (Round your standard deviation to four decimal places.) mean: 0.05 standard deviation: 0.0109 (b) Is the sampling distribution of p? approximately normal for random samples of size n = 100? Explain. The sampling distribution of p? is not approximately normal because np is less than 10. (c) Suppose that the sample size is n = 400 rather than n = 100. What are the values for the mean and standard deviation when n = 400? (Round your standard deviation to four decimal places.) mean: 0.05 standard deviation: 0.0218 Does the change in sample size affect the mean and standard deviation of the sampling distribution of p?? If not, explain why not. (Select all that apply.) When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size. When the sample size increases, the standard deviation decreases. (d) Is the sampling distribution of p? approximately normal for random samples of size n = 400? Explain. The sampling distribution of p? is not approximately normal because only np is at least 10.

A news article estimated that only 5% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05.

(a) A random sample of n = 100 people will be selected from this population and p?, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p?? (Round your standard deviation to four decimal places.)
mean: 0.05
standard deviation: 0.0109

(b) Is the sampling distribution of p? approximately normal for random samples of size n = 100? Explain.
The sampling distribution of p? is not approximately normal because np is less than 10.

(c) Suppose that the sample size is n = 400 rather than n = 100. What are the values for the mean and standard deviation when n = 400? (Round your standard deviation to four decimal places.)
mean: 0.05
standard deviation: 0.0218

Does the change in sample size affect the mean and standard deviation of the sampling distribution of p?? If not, explain why not. (Select all that apply.)
When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size.
When the sample size increases, the standard deviation decreases.

(d) Is the sampling distribution of p? approximately normal for random samples of size n = 400? Explain.
The sampling distribution of p? is not approximately normal because only np is at least 10.

A news article estimated that only 5% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05.

(a) A random sample of n = 100 people will be selected from this population and p?, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution of p?? (Round your standard deviation to four decimal places.)
mean: 0.05
standard deviation: 0.0109

(b) Is the sampling distribution of p? approximately normal for random samples of size n = 100? Explain.
The sampling distribution of p? is not approximately normal because np is less than 10.

(c) Suppose that the sample size is n = 400 rather than n = 100. What are the values for the mean and standard deviation when n = 400? (Round your standard deviation to four decimal places.)
mean: 0.05
standard deviation: 0.0218

Does the change in sample size affect the mean and standard deviation of the sampling distribution of p?? If not, explain why not. (Select all that apply.)
When the sample size increases, the mean stays the same. The sampling distribution is always centered at the population mean, regardless of sample size.
When the sample size increases, the standard deviation decreases.

(d) Is the sampling distribution of p? approximately normal for random samples of size n = 400? Explain.
The sampling distribution of p? is not approximately normal because only np is at least 10.

Added by Mary W.

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