Exam 8: Sampling Methods and the Central Limit Theorem

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 _____________.

A __________________ assumes that each item or individual in the population has an equal chance of being included.

If the size of a sample equals the size of the population, the sampling error is ________.

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 standard error of the mean?

Sampling is required when crash testing cars because the products are __________.

Sampling error is the difference between a sample statistic and its corresponding _________.

The standard deviation of the sampling distribution of the sample means is called the ______________.

A sampling distribution of the means is a probability distribution consisting of all possible sample means of a given sample size selected from a population.

Sampling from a population may be preferred because, contacting or listing the entire population would be too ___________ consuming.

A population consists of 15 values. How many samples of size 10 are possible?

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 less than 95?

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

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 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?

The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large number of observations, the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation of 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

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. Compare the dispersion in the population with that of the sample means.

The true sampling error is usually not known because ________.

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?

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?

If the sampling distribution of the sample means approximates a normal distribution, then the population is normally distributed.