Sampling Distribution Center and Variability

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population Distribution

• The Distribution of the Sample

• The Distribution of the Sample Means (Sampling Distribution)

What happens to the shape of a sampling distribution of sample means as the sample size (n) increases?

• It becomes narrower (less variability) and bimodal.

• It becomes narrower (less variability) and more normal.

• It becomes wider (more variability) and skewed right.

• It becomes wider (more variability) and more normal.

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population Distribution

• The Distribution of the Sample

• The Distribution of the Sample Means (Sampling Distribution)

The mean of a population is μ = 200 the standard deviation is σ = 20. Random samples of size 25 are taken from this population.

What is the mean of the sampling distribution?

• 200

• 16

• 25

• 4

Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?

• A sample of size 25 will produce more variability of the estimator than a sample of size 50.

• A sample of size 25 will produce less variability of the estimator than a sample of size 50.

• A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.

• A sample of size 25 will produce a more biased estimator than a sample of size 50.

• A sample of size 25 will produce a less biased estimator than a sample of size 50.

A simple random sample of 1000 Americans found that 62% were satisfied with the service provided by the dealer from which they bought their car.  A simple random sample of 1000 Canadians found that 59% were satisfied with the service provided by the dealer from which they bought their car.  The sampling variability associated with these statistics is

• exactly the same

• not exactly the same, but very close

• much smaller for the sample of Canadians because the population of Canad is much smaller than that of the United States, hence the sample is a larger proportion of the population.

• smaller for the sample of Canadians because the percent satisfied was smaller than that of Americans.

When x̅ differs from sample to sample, we say this is an example of

• variability among the samples

• bias among the samples

• not having large enough sample sizes

• poor survey techniques

Researchers will conduct a study of the television-viewing habits of children. They will select a random sample of children and record the number of hours of television the children watch per week. Which of the following statements is correct?

• A sample of size 25 will produce more variability in the sampling distribution than a sample of size 50 will.

• A sample of size 25 will produce less variability in the sampling distribution than a sample of size 50 will.

• A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator.

• A sample of size 25 will produce a more normal curve than a sample of size 50 will.

• A sample of size 25 will produce a less biased estimator than a sample of size 50.

The mean of a population is μ = 200 the standard deviation is σ = 20. Random samples of size 25 are taken from this population.

What is the standard deviation of the sampling distribution?

• 200

• 16

• 25

• 4