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Exam 8: Sampling Methods and the Central Limit Theorem

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Question 1

True/False

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The central limit theorem states that if the sample size, n, is sufficiently large, the sampling distribution of the means will be approximately normal, even when the population is skewed or uniform.

A) True
B) False

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Question 2

Multiple Choice

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A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18-21 years of age, a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September. What is the sample size?

A) 4
B) 100
C) 400
D) 1

E) C) and D)
F) None of the above

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Question 3

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The American Auto Association reports the mean price per gallon of regular gasoline is $3.10, with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed. What is the probability that the difference between the sample mean and the population mean is less than 0.01?

To study the population of consumer perceptions of new technology, sampling of the population is preferred over surveying the population because _________.

The standard error of the mean is also called sampling error.

For a distribution of sample means constructed by sampling 5 items from a population of 15, ___________.

In practice, researchers collect a sample of size "n" and compute point estimates of population parameters. How can sampling error be reduced?

How is the central limit theorem helpful when computing probabilities?

In the sampling distribution of the sample means, the standard error of the mean will vary according to the size of the sample. As the sample size n gets larger, the variability of the sampling distribution of the means gets _____________.

When computing probabilities for the sampling distribution of the sample mean, the z-statistic is computed as .

A university has 1,000 computers available for students to use. Each computer has a 250-gigabyte hard drive. The university wants to estimate the space occupied on the hard drives. A random sample of 100 computers showed a mean of 115 gigabytes used with a standard deviation of 20 gigabytes. What is the probability that a sample mean is between 111 and 119 gigabytes?

Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive.

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is between 57,000 and 63,000 miles?

When testing the safety of cars using crash tests, a sample of one or two cars is used because ___________.

Suppose we select every fifth invoice in a file. What type of sampling is this?

When deciding to collect sample information rather than collecting information from the population, the amount of time required to collect the information is unimportant.

The true sampling error is usually not known because ________.

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18-21 years of age, a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September. What is the number of samples?

LongLast Inc. produces car batteries. The mean life of these batteries is 60 months. The distribution of the battery life closely follows the normal probability distribution with a standard deviation of eight months. As a part of its testing program, LongLast tests a sample of 25 batteries. What proportion of the samples will have a mean useful life of more than 56 months?

The American Auto Association reports the mean price per gallon of regular gasoline is $3.10, with a population standard deviation of $0.20. Assume a random sample of 16 gasoline stations is selected and their mean cost for regular gasoline is computed. What is the standard error of the mean in this experiment?