Exam 8: Sampling Methods and the Central Limit Theorem

A population consists of 12 values. How many samples of size six are possible?

If 40 samples of size 21 were selected from a population of 22,493, we would expect the mean of the sample means and the population mean to be close but not exactly equal.

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?

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 greater than 120 gigabytes?

The Intelligence Quotient (IQ) test scores for adults are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability we could select a sample of 50 adults and find the mean of this sample is between 95 and 105?

Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called?

When using stratified random sampling, the sampling error will be zero.

Sampling from a population may be preferred, because studying all the items in a population may be too ____________.

Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes and the standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the mean time to complete a tax form?

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 part of its testing program, LongLast tests a sample of 25 batteries. What is the standard error of the mean?

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

In cluster sampling, a population is divided into subgroups called clusters and a sample is randomly selected from each cluster.

The Office of Student Services at a large western state university maintains information on the study habits of its full-time students. Their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. The hours studied follows the normal distribution with a standard deviation of six hours. Suppose we select a random sample of 144 current students. What is the probability that the mean of this sample is less than 19.25 hours?

Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20 and the sample standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21?

What are the two population parameters that specify the location and dispersion for the sampling distribution of the mean?

For populations scattered in a wide area, the preferred technique for sampling is ___________.

The mean of all possible sample means is equal to the population mean.

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

A population consists of the following four values: 8, 10, 12, and 16. From this population, there are six different samples of size 2. The means of the six samples of size 2 are 9, 10, 12, 11, 13, and 14. Compute the mean of the distribution of the sample means and the population mean. What is true about the two values?

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?