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Exam 8: Sampling Distributions and Estimation

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Question 31

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Approximately 95 percent of the population X values will lie within the 95 percent confidence interval for the mean.

A) True
B) False

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Question 32

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Professor York randomly surveyed 240 students at Oxnard University and found that 150 of the students surveyed watch more than 10 hours of television weekly. Develop a 95 percent confidence interval to estimate the true proportion of students who watch more than 10 hours of television each week. The confidence interval is:

A) .533 to .717
B) .564 to .686
C) .552 to .698
D) .551 to .739

E) B) and D)
F) B) and C)

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Question 33

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The Central Limit Theorem says that a histogram of the sample means will have a bell shape, even if the population is skewed and the sample is small.

Assuming that π = .50 is a quick and conservative approach to use in a sample size calculation for a proportion.

The efficiency of an estimator depends on the variance of the estimator's sampling distribution.

As n increases, the width of the confidence interval will decrease, ceteris paribus.

A marketing firm is asked to estimate the percentage of existing customers who would purchase a "digital upgrade" to their basic cable TV service. The firm wants 99 percent confidence and an error of ± 5 percent. What is the required sample size (to the next higher integer) ?

To estimate the required sample size for a proportion, one method is to take a small pilot sample to estimate π and then apply the sample size formula.

In constructing a confidence interval, the finite population correction factor (FPCF) can be ignored if samples of 12 items are drawn from a population of 300 items.

When the sample standard deviation is used to construct a confidence interval for the mean, we would use the Student's t distribution instead of the normal distribution.

The expected value of an unbiased estimator is equal to the parameter whose value is being estimated.

The sample proportion is in the middle of the confidence interval for the population proportion:

Last week, 108 cars received parking violations in the main university parking lot. Of these, 27 had unpaid parking tickets from a previous violation. Assuming that last week was a random sample of all parking violators, find the 95 percent confidence interval for the percentage of parking violators that have prior unpaid parking tickets.

A random sample of 160 commercial customers of PayMor Lumber revealed that 32 had paid their accounts within a month of billing. The 95 percent confidence interval for the true proportion of customers who pay within a month would be:

What is the approximate width of an 80 percent confidence interval for the true population proportion if there are 12 successes in a sample of 80?

In a sample size calculation, if the confidence level decreases, the size of the sample needed will increase.

The Central Limit Theorem (CLT) :

The Central Limit Theorem guarantees an approximately normal sampling distribution when n is sufficiently large.

Concerning confidence intervals, which statement is most nearly correct?

A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is: