Exam 7: Sampling and Sampling Distributions

The size of a sample can be selected by first determining the desired standard error and then using the formula to calculate n.

A simple random sample is one where each member of the population has a known chance (this may differ from one member to another)or probability of being chosen.

Ideally,we prefer estimates that have large standard errors.

In systematic sampling,one of the first k members is selected randomly,and then every k^th member after this one is selected.The value k is called the sampling interval and equals the ratio N / n,where N is the population size and n is the desired sample size.

The opportunity for sampling error is decreased by:

(A)Compute the mean,median,and standard deviation of the annual salaries for the 52 employees in the given frame. (B)Use Excel to choose a systematic sample of size 13 from the frame of annual salaries. (C)Compute the mean,median,and standard deviation of the annual salaries for the 13 employees included in your systematic sample in (B) (D)Compare your statistics in (C)with your computed descriptive measures for the frame in (A).Is your systematic sample representative of the frame with respect to the annual salary variable? (E)Assume that we wish to stratify these employees by the number of years of post-secondary education,select such a stratified sample of size 15 with approximately proportional sample sizes. (F)Compute the mean,median,and standard deviation of the annual salaries for the 15 employees included in your stratified sample in (E). (G)Compare these statistics in (F)with your computed descriptive measures for the frame obtained in (A).Is your stratified sample representative of the frame with respect to the annual salary variable?

(A)Technically,this process does not yield a random sample of the books in the store.Why not? (B)How could a truly random sample be obtained?

(A)Do you think she has obtained a true random sample? (B)What average price could she report,based on the above sample? (C)What average price range could she report,based on the above sample? (D)Do you see any issues with reporting the range calculated for (C)?

The sampling distribution of any point estimate (such as the sample mean or proportion)is the distribution of the point estimates we would obtain from all possible samples of a given size drawn from the population.

The accuracy of the point estimate is measured by its:

In stratified sampling with proportional sample sizes,the proportion of each stratum selected differs from stratum to stratum.

Cluster sampling is often less convenient and more costly than other random sampling methods.

The finite population correction factor, ,should generally be used when:

A sample of size 20 is selected at random from a population of size N.If the finite population correction factor is 0.9418,then N must be 169.

The opportunity for nonsampling error is increased by:

(A)Using these 50 students as the frame,use Excel to generate a simple random sample of size 10 from this frame. (B)Compute the mean scores in the frame and the simple random sample you generated in (A). (C)Compare the mean scores you computed in (B).Is your simple random sample a good representative of the frame? Why or why not? (D)Using these 50 students as the frame,use Excel to generate a systematic sample of size 10 from this frame. (E)Compare the mean scores in the frame with that in the systematic sample in (D).What do you conclude?

Which of the following statements are correct?

Non-truthful response is a particular problem when:

The probability of being chosen in a simple random sample of size n from a population of size N is:

A list of all members of the population from which we can choose a sample is called a frame,and the potential sample members are called sampling units.