Ch. 7 Sampling and Sampling Distributions

cluster sampling

A probability sampling method in which the population is first divided into clusters and then a simple random sample of the clusters is taken.

systematic sampling

A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter.

unbiased

A property of a point estimator that is present when the expected value of the point estimator is equal to the population parameter it estimates.

consistency

A property of a point estimator that is present whenever larger sample sizes tend to provide point estimates closer to the population parameter.

random sample

A random sample from an infinite population is a sample selected such that the following conditions are satisfied: (1) Each element selected comes from the same population; (2) each element is selected independently.

sample statistic

A sample characteristic, such as a sample mean "x-bar", a sample standard deviation "s", a sample proportion "p-bar", and so on. The value of the sample statistic is used to estimate the value of the corresponding population parameter.

simple random sample

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size n has the same probability of being selected.

target population

the population for which statistical inference such as point estimates are made. it is important for the target population to correspond as closely as possible to the sampled population.

sampled population

the population from which the sample is taken

standard error

the standard deviation of a point estimator

finite population correction factor

the term √((N-1)/(n-1)) that is used in the formulas for standard deviation of x bar and p bar whenever a finite population, rather than an infinite population, is being sampled. the generally expected rule of thumb is to ignore this when n/N ≤ .05

point estimate

the value of a point estimator used in a particular instance as an estimate of a population parameter

37. A population characteristic, such as a population mean, is called a. a statistic b. a parameter c. a sample d. the mean deviation

b. a parameter

20. In point estimation a. data from the population is used to estimate the population parameter b. data from the sample is used to estimate the population parameter c. data from the sample is used to estimate the sample statistic d. the mean of the population equals the mean of the sample

b. data from the sample is used to estimate the population parameter

30. The sampling error is the a. same as the standard error of the mean b. difference between the value of the sample mean and the value of the population mean c. error caused by selecting a bad sample d. standard deviation multiplied by the sample size

b. difference between the value of the sample mean and the value of the population mean

2. Parameters are a. numerical characteristics of a sample b. numerical characteristics of a population c. the averages taken from a sample d. numerical characteristics of either a sample or a population

b. numerical characteristics of a population

44. The purpose of statistical inference is to provide information about the a. sample based upon information contained in the population b. population based upon information contained in the sample c. population based upon information contained in the population d. mean of the sample based upon the mean of the population

b. population based upon information contained in the sample

24. The probability distribution of the sample mean is called the a. central probability distribution b. sampling distribution of the mean c. random variation d. standard error

b. sampling distribution of the mean

40. The standard deviation of a point estimator is called the a. standard deviation b. standard error c. point estimator d. variance of estimation

b. standard error

26. The standard deviation of all possible values is called the a. standard error of proportion b. standard error of the mean c. mean deviation d. central variation

b. standard error of the mean

33. The probability distribution of all possible values of the sample mean is a. the probability density function of b. the sampling distribution of c. the grand mean, since it considers all possible values of the sample mean d. one, since it considers all possible values of the sample mean

b. the sampling distribution of

15. The closer the sample mean is to the population mean, a. the larger the sampling error b. the smaller the sampling error c. the sampling error equals 1 d. None of these alternatives is correct.

b. the smaller the sampling error

21. The sample statistic s is the point estimator of a. µ b. σ

b. σ

23. If we consider the simple random sampling process as an experiment, the sample mean is a. always zero b. always smaller than the population mean c. a random variable d. exactly equal to the population mean

c. a random variable

29. Whenever the population has a normal probability distribution, the sampling distribution of is a normal probability distribution for a. only large sample sizes b. only small sample sizes c. any sample size d. only samples of size thirty or greater

c. any sample size

10. In computing the standard error of the mean, the finite population correction factor is used when a. N/n > 0.05 b. N/n 0.05 c. n/N > 0.05 d. n/N 30

c. n/N > 0.05

11. Convenience sampling is an example of a. probabilistic sampling b. stratified sampling c. nonprobabilistic sampling d. cluster sampling

c. nonprobabilistic sampling

28. As the sample size becomes larger, the sampling distribution of the sample mean approaches a a. binomial distribution b. Poisson distribution c. normal distribution d. chi-square distribution

c. normal distribution

35. Which of the following is(are) point estimator(s)? a. σ b. µ c. s d. α

c. s

17. As the sample size increases, the a. standard deviation of the population decreases b. population mean increases c. standard error of the mean decreases d. standard error of the mean increases

c. standard error of the mean decreases

13. Stratified random sampling is a method of selecting a sample in which a. the sample is first divided into strata, and then random samples are taken from each stratum b. various strata are selected from the sample c. the population is first divided into strata, and then random samples are drawn from each stratum d. None of these alternatives is correct.

c. the population is first divided into strata, and then random samples are drawn from each stratum

25. The expected value of the random variable is a. the standard error b. the sample size c. the size of the population d. None of these alternatives is correct.

d. None of these alternatives is correct.

41. A single numerical value used as an estimate of a population parameter is known as a. a parameter b. a population parameter c. a mean estimator d. a point estimate

d. a point estimate

36. A probability distribution for all possible values of a sample statistic is known as a. a sample statistic b. a parameter c. simple random sampling d. a sampling distribution

d. a sampling distribution

16. Since the sample size is always smaller than the size of the population, the sample mean a. must always be smaller than the population mean b. must be larger than the population mean c. must be equal to the population mean d. can be smaller, larger, or equal to the population mean

d. can be smaller, larger, or equal to the population mean

34. Which of the following sampling methods does not lead to probability samples? a. stratified sampling b. cluster sampling c. systematic sampling d. convenience sampling

d. convenience sampling

12. Which of the following is an example of nonprobabilistic sampling? a. simple random sampling b. stratified simple random sampling c. cluster sampling d. judgment sampling

d. judgment sampling

9. The probability distribution of all possible values of the sample proportion is the a. probability density function of b. sampling distribution of c. same as , since it considers all possible values of the sample proportion d. sampling distribution of

d. sampling distribution of

relative efficiency

given two unbiased point estimators of the same population parameter, the point estimator with the smaller standard error is more efficient

frame

A listing of the elements the sample will be selected from.

judgment sampling

A nonprobability method of sampling whereby elements are selected for the sample based on the judgment of the person doing the study.

convenience sampling

A nonprobability method of sampling whereby elements are selected for the sample on the basis of convenience.

parameter

A numerical characteristic of a population, such as a population mean μ, a population standard deviation σ, a population proportion p, and so on.

sampling with replacement

Once an element has been included in the sample, it is removed from the population and cannot be selected a second time.

sampling without replacement

Once an element has been included in the sample, it is removed from the population and cannot be selected a second time.

point estimator

The sample statistic, such as xbar, s, or pbar , that provides the point estimate of the population parameter.

sampling distribution

a probability distribution consisting of all possible values of a sample statistic

stratified random sampling

a probability sampling method in which a population is divided into subpopulation groups called strata; individuals are then randomly sampled from each of the strata

central limit theorem

a theorem that enables one to use the normal probability distribution to approximate the sampling distribution of x bar whenever the sample size is large

42. The sample statistic, such as , s, or , that provides the point estimate of the population parameter is known as a. a point estimator b. a parameter c. a population parameter d. a population statistic

a. a point estimator

39. A sample statistic, such as a sample mean, is known as a. a statistic b. a parameter c. the mean deviation d. the central limit theorem

a. a statistic

18. A simple random sample from an infinite population is a sample selected such that a. each element is selected independently and from the same population b. each element has a 0.5 probability of being selected c. each element has a probability of at least 0.5 of being selected d. the probability of being selected changes

a. each element is selected independently and from the same population

5. Sampling distribution of is the a. probability distribution of the sample mean b. probability distribution of the sample proportion c. mean of the sample d. mean of the population

a. probability distribution of the sample mean

22. The sample mean is the point estimator of a. µ b. σ

a. µ