Exam 8: Sampling Methods and the Central Limit Theorem

What is the difference between a sample mean and the population mean called?

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

Auditors may select every 20^th file starting with the 5^th file in the top drawer. Then, file numbers 25, 45, 65, 85, . . . are selected. This type of sampling is called ___________.

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

The items or individuals of the population are arranged in a file drawer alphabetically by date received. A random starting point is selected and then every k^th member of the population is selected for the sample. This sampling method is called systematic random sampling.

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

A total of _______ different samples of size 3 can be collected from a population of 10 items.

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

Based on the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the size of the sample is sufficiently large.

According to the central limit theorem, _______________.

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?

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 between 19 hours and 20 hours?

In stratified random sampling, a population is divided into strata using naturally occurring geographic or other boundaries. Then, strata are randomly selected and a random sample is collected from each strata.

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

The ___________ sampling method is best to use if the population can be divided into two or more homogeneous subgroups.

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 200 gigabytes?

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

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 less than 56 months?

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

The central limit theorem states that for a sufficiently large sample the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to σ² and the variance equal to σ^2/n.