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Exam 8: Sampling Methods and the Central Limit Theorem

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Question 1

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It is often not feasible to study the entire population because it is impossible to observe all the items in the population.

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B) False

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Question 2

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A population consists of 10 values. How many samples of size six are possible?

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210
Explanation: We ...

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If the size of a sample equals the size of the population, we would not expect any error in estimating the population parameter.

An experiment involves selecting a random sample of 256 middle managers for study. One item of interest is their annual income. The sample mean is computed to be $35,420, and the sample standard deviation is $2,050. What is the sample standard error of the mean?

The American Auto Association reports that 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?

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 we select a sample of 40 tires and use a simulator to determine the tread life. What is the standard error of the mean?

The central limit theorem allows us to use a z-statistic to compute probabilities for the sampling distribution of the sample mean.

A statewide sample survey is to be made. First, the state is subdivided into counties. Seven counties are selected at random and further sampling is concentrated on these seven counties. What type of sampling is this?

The process of making statements about a population based on a sample from the population is called _______________.

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18 to 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 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 standard error of the mean?

To collect a sample, a population is first divided into subgroups and then a sample is selected from each subgroup. This is called _________ sampling.

According to the central limit theorem, ____________.

What are the two population parameters that specify the location and dispersion for a normal distribution?

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?

Which of the following is the standard error of the mean?

The American Auto Association reports that 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 likelihood the sample mean is greater than $3.08?

For a given population with a normal probability distribution, the sampling distribution of is a normal probability distribution for:

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18 to 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?

When all the items in a population have an equal chance of being selected for a sample, the process is called _________________.