Exam 8: Sampling Methods and the Central Limit Theorem

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

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 likelihood the sample mean is greater than $3.08?

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

What type of sampling is it when a population is first divided into subgroups and then a sample is selected from each subgroup? _________

According to the central limit theorem,

What is a characteristic of a population called? _______________

Sometimes, sampling from a population may be preferred because collecting statistics may require that products be __________.

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 8 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?

If the sample size equals the population size, what is the sampling error? _________

Suppose a research firm conducted a survey to determine the average amount of money 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?

For populations scattered in a wide area, what is the preferred technique for sampling? ____________

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.

A population consists of 14 values. How many samples of size five are possible?

In practice, researchers collect a sample of size "n" and compute point estimates of population parameters. How can sampling error be reduced?

A population consists of the following four values: 8, 10, 12, and 16. From this population, there are 6 different samples of size 2. The means of the 6 samples of size 2 are: 9,10,12,11,13, and 14. Compare the dispersion in the population with that of the sample means.

If a population is normally distributed, then the sampling distribution of the sample means will be __________________________.

Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive.

The Central Limit Theorem states that if the sample size, n, is sufficiently large, the sampling distribution of the means will be approximately normal, even when the population is skewed or uniform.

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women, 18-21 years of age, a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September.

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students study per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the probability of finding a sample mean less than 18 hours?