Exam 8: Sampling Methods and the Central Limit Theorem

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the probability that the mean completion time will be more than 120 minutes?

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?

How is the Central Limit Theorem helpful when computing probabilities?

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

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, 13.33. Compute the mean of the distribution of the sample means and the population mean. What is true about the two values?

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

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

The American Auto Association reports 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 sample mean is between $2.98 and $3.12?

When testing the safety of cars using crash tests, a sample of 1 or 2 cars is used because

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

To study the population of consumer perceptions of new technology, sampling of the population is preferred over surveying the population because

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 $\sigma$ ² and the variance equal to $\sigma$ ^2/n.

The true sampling error is usually not known because

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

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 larger.