Exam 8: Sampling Methods and the Central Limit Theorem

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 that the mean of this sample exceeds 104?

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

The standard error of the mean is directly related to the sample size.

As the sample size (n) increases, the spread or dispersion of the distribution of the sample means __________.

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

As the size of the sample increases, what happens to the shape of the distribution of sample means?

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

The standard error of the mean measures the dispersion of the sampling distribution of the sample mean.

Sampling error is defined as _________.

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

For the sampling distribution of sample means, sampling error will decrease as sample size increases.

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

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

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.

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

A population consists of the following five values: 3, 8, 11, 13, and 16. From this population, there are 10 different samples of size 3. The means of the 10 samples of size 3 are: 7.33, 8, 9, 9, 10, 10.67, 10.67, 11.67, 12.33, and 13.33. Compute the mean of the distribution of the sample means and the population mean. What is true about the two values?

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?

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 likelihood of finding that the sample mean is between 59,050 and 60,950?

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?