8.3

A news article estimated that only5% of thoseages 65and 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 Americansages 65and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is0.05.

(a)

A random sample ofn= 100

people will be selected from this population andp, the proportion of people who prefer to watch online, will be calculated. What are the mean and standard deviation of the sampling distribution ofp? (Round your standard deviation to four decimal places.)

mean=

standard deviation=

(b)

Is the sampling distribution ofpapproximately normal for random samples of sizen= 100?

Explain. (Select all that apply.)

the sampling distribution ofpis approximately normal

the sampling distribution ofpis not approximately normal

npis less than 10

npequals 10

npis greater than 10

n(1p) is less than 10

n(1p) equals 10

n(1p) is greater than 10

(c)

Suppose that the sample size isn= 400

rather thann= 100.

What are the values for the mean and standard deviation whenn= 400?

(Round your standard deviation to four decimal places.)

mean=

standard deviation=

Does the change in sample size affect the mean and standard deviation of the sampling distribution ofp? If not, explain why not. (Select all that apply.)

When the sample size increases, the mean increases.

When the sample size increases, the mean decreases.

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 increases.

When the sample size increases, the standard deviation decreases.

When the sample size increases, the standard deviation stays the same. The standard deviation of the sampling distribution is always the same as the standard deviation of the population distribution, regardless of sample size.

(d)

Is the sampling distribution ofpapproximately normal for random samples of sizen= 400?

Explain. (Select all that apply.)

the sampling distribution ofpis approximately normal

the sampling distribution ofpis not approximately normal

npis less than 10

npequals 10

npis greater than 10

n(1p) is less than 10

n(1p) equals 10

n(1p) is greater than 10