SOCI 3307 Exam 2

Which of the following is/are true with respect to a random sample?

a. All of these

b. The selection of each case is independent of the selection of other cases

c. In the selection of cases, all combinations are possible

d. Every case has an equal chance of being selected

a. all of these

Assume that you want to conduct a study of registered voters in your local community. As a starting point, you get a list of registered voters from the local election bureau. The correct term for the list is:

a. a sample selection list

b. a sampling listing

c. a statement of the population

d. a sampling frame

d. a sampling frame

Assume that the population of your customers divided as follows: 40% male and 60% female. If you were to take a random sample, which of the following would be possible?

a. You could get a sample that was approximately 40% male and 60% female

b. You could get a sample that was approximately 50% male and 50% female

c. You could get a sample that was approximately 10% male and 90% female

d. All of these are possible

d. All of these are possible

In the Central Limit Theorem, n refers to:

a. the sample mean

b. the standard deviation

c. the size of each sample used to construct the sampling distribution

d. the number of samples used to construct the sampling distribution

c. the size of each sample used to construct the sampling distribution

The term, sampling frame, refers to:

a. a description of the population in terms of its major characteristics

b. the design of your sample in a research project

c. the frame of reference for your sample design

d. a physical representation of the population

d. a physical representation of the population

Assume the following: The mean of the population = 45.21 and the mean of a random sample taken from that population = 47.83. Assuming that the difference between the two values is due to chance, we can say that the difference is the result of:

a. population/sample error

b. a chance sample

c. sampling risk

d. sampling error

d. sampling error

In the Central Limit Theorem, σ represents:

a. Cannot determine based upon the information given

b. the standard deviation of the population

c. the standard deviation of the sample

d. the standard deviation of the sampling distribution

b. the standard deviation of the population

Assume that you have taken sample after sample after sample, each time calculating and recording the sample median. Further assume that you have now plotted all of the sample medians. Your plot of sample medians would be referred to as a:

a. a sample distribution

b. repetitive distribution of sample medians

c. uniform distribution of sample medians

d. sampling distribution of sample medians

d. sampling distribution of sample medians

Assume that you have constructed a sampling distribution of sample means, based upon repeated random samples of 100 cases. Further assume that the standard deviation of the population (σ) from which the samples are taken is equal to 36. What will be the value of the standard error of the mean?

a. Cannot determine from the information given

b. The square root of 36, or 6

c. 360

d. 3.6

d. 3.6

Which of the following is true with respect to the sampling distribution of sample means?

a. None of these are true

b. the standard deviation of the population is unknown

c. the standard deviation of the distribution is referred to as the standard error of the mean

d. the mean of the sampling distribution is not related to the mean of the population from which the samples were taken

c. the standard deviation of the distribution is referred to as the standard error of the mean

According to the central limit theorem, the mean of the sampling distribution of sample means is equal to:

a. mu (the mean of the population)

b. the number of cases that are selected

c. a Z score of +/- 1.96

d. a Z score of +/- 2.58

a. mu (the mean of the population)

In the Central Limit Theorem, the standard error refers to the:

a. none of these

b. the standard deviation of the population

c. the standard deviation of the sampling distribution of sample means

d. mu (the mean of the population

c. the standard deviation of the sampling distribution of sample means

According to the Central Limit Theorem, how is the standard error of the mean calculated?

a. cannot determine on the basis of the information provided.

b. the value of mu, divided by n

c. the value of sigma (σ), divided by the square root of n

d. the value of sigma (σ), multiplied by the square root of n

c. the value of sigma (σ), divided by the square root of n

A key element in the Central Limit Theorem is the notion of ________ random samples of size ________ .

a. 100; 100

b. at least three; 10

c. repeated; n

d. 25; 200

c. repeated; n

A key element in the Central Limit Theorem is the notion that the sampling distribution will approach ________ .

a. a skewed distribution

b. the size of the population

c. the mean of the sampling distribution

d. a normal distribution

d. a normal distribution

Assume the following: A sampling distribution of sample means was constructed using samples of 100 cases. The standard deviation of the population from which the samples were selected is 50. What would be the value of the standard error of the mean?

a. Cannot determine on the basis of the information given

b. 2

c. .5

d. 5

d. 5

Assume the following: A sampling distribution of sample means was constructed using samples of 25 cases. Then, a sampling distribution of sample means was constructed from the same population, but using samples of 100. How would the standard errors differ?

a. Cannot determine on the basis of the information given

b. The standard errors would not differ; they would be the same.

c. The standard error would be smaller in the second sampling distribution.

d. The standard error would be larger in the second sampling distribution.

c. The standard error would be smaller in the second sampling distribution.

When conducting a confidence interval for the mean with sigma known, the standard error of the mean is derived by:

a. adding the mode and the median of the distribution

b. subtracting the sampling error from the sample size

c. multiplying the sample mean by µ

d. dividing σ by the square root of n

d. dividing σ by the square root of n

When constructing a confidence interval for the mean with sigma unknown, which distribution do you use?

a. t distribution

b. Distribution of x

c. Z distribution

d. None of these

a. t distribution

When constructing a confidence interval for the mean with sigma known, which distribution do you use?

a. t distribution

b. Distribution of x

c. Z distribution

d. None of these

c. Z distribution

When constructing a confidence interval for the mean with sigma unknown, the standard error of the mean is derived by:

a. dividing s by the square root of n

b. adding the upper and lower values of the range of the distribution and dividing the total by the mode of the distribution

c. using the same method that is used to calculate the standard error of the mean when sigma is known

d. none of these

a. dividing s by the square root of n

When constructing a confidence interval for the mean, statisticians typically select one or the other of which levels of confidence?

a. 68% and 80%

b. 80% and 90%

c. 50% and 68%

d. 95% and 99%

d. 95% and 99%

Assume that you have constructed a confidence interval for the mean, using a 95% level of confidence. Your calculations resulted in a lower limit of 16.43 and an upper limit of 21.82. Which of the following is the correct interpretation of the construction of a confidence interval for the mean?

a. The range of the population mean is between 16.43 and 21.82.

b. I estimate that the mean of the population is somewhere between 16.43 and 21.82, and I have used a method that will produce a correct estimate 95 times out of 100.

c. I estimate that 95% of the time, the mean of the population will be somewhere between 16.43 and 21.82.

d. The mean of the sample falls somewhere between 16.43 and 21.82.

b. I estimate that the mean of the population is somewhere between 16.43 and 21.82, and I have used a method that will produce a correct estimate 95 times out of 100.

In the construction of a confidence interval for the proportion, the expression 1-p in the formula represents:

a. 1 plus the observed proportion (i.e., if p =.46 then 1+ .46 =1.46)

b. a Z score

c. 1 minus the observed proportion (i.e., if p =.46 then 1-.46 =.54)

d. none of these

c. 1 minus the observed proportion (i.e., if p =.46 then 1-.46 =.54)

Assume that you are going to construct a confidence interval for the mean using a 95% level of confidence. If you increased your sample size, what would happen to the width of the interval?

a. It would decrease

b. It would remain the same

c. It would increase

d. Cannot determine based upon the information provided

a. It would decrease

Assume that you are going to construct a confidence interval for the proportion using a 95% level of confidence. If at the last minute, however, you decided to go with a 99% level of confidence, what would happen to the width of the interval?

a. It would decrease

b. It would remain the same

c. It would increase

d. Cannot determine based upon the information provided

c. It would increase

Assume that you are going to construct a confidence interval for the proportion using a 99% level of confidence. If you increased your sample size, what would happen to the width of the interval?

a. It would decrease

b. It would remain the same

c. It would increase

d. Cannot determine based upon the information provided

a. It would decrease

Assume that you are going to construct a confidence interval for the mean with sigma unknown, using a 95% level of confidence with a sample of 21 cases. What would the appropriate number of degrees of freedom to use?

a. 21

b. 19

c. 20

d. Cannot determine based upon the information provided

c. 20

Assume that you are going to construct a confidence interval for the mean with sigma unknown, using a 99% level of confidence and a sample of 25 cases. Based upon the information in Appendix B of your text, what would be the appropriate t value to use?

a. 2.797

b. 2.580

c. 2.064

d. Cannot determine based upon the information provided

a. 2.797

Assume that you are going to construct a confidence interval for the mean with sigma unknown, using a 95% level of confidence and a sample of 81 cases. Based upon the information in Appendix B of your text, what would be the appropriate t value to use?

a. 1.990

b. 1.960

c. 2.639

d. Cannot determine based upon the information provided

a. 1.990

When constructing a confidence interval for the mean, there is a difference in the approach used when sigma is known, as opposed to when sigma is unknown. Which of the following best describes the difference?

a. When sigma is known, the standard error is estimated, but it is calculated when sigma is known.

b. When sigma is unknown, the standard error is estimated, and it is also estimated when sigma is known.

c. When sigma is unknown, the standard error is estimated, but it is calculated when sigma is known.

d. Cannot determine based upon the information provided

c. When sigma is unknown, the standard error is estimated, but it is calculated when sigma is known.

A In terms of a confidence interval for the mean, as the level of confidence increases, what happens to the precision of the estimate?

a. It decreases

b. It remains the same

c. It increases

d. Cannot determine without knowing the value of the mean

a. It decreases

In terms of a confidence interval for the mean with σ unknown, as the level of confidence increases, what happens to the t value that is used to develop the interval?

a. It decreases

b. It remains the same

c. It increases

d. Cannot determine without knowing the value of the mean

c. It increases

When using Appendix B in your text (Family of t Distributions) to construct a confidence interval for the mean, how are degrees of freedom calculated?

a. n-1

b. N+1

c. N-1

d. n+1

a. n-1

Given the information in Appendix B (the Family of t Distributions), and assuming a constant level of confidence, what happens to the value of t as the number of degrees of freedom increases?

a. The value of t decreases

b. The value of t remains the same

c. The value of t increases

d. Cannot determine without knowing the value of the mean

a. The value of t decreases

As the number of cases used to develop a confidence interval for the proportion increases, the margin of error:

a. decreases

b. remains the same

c. increases

d. cannot determine of the basis of the information provided

a. decreases

Select the proper interpretation for the following finding concerning the percentage of voters who plan to vote for Candidate Jones: A 95% confidence interval for the proportion reflects lower and upper limits of 52% and 57%.

a. Candidate Jones can be expected to win with at least 51% of the vote, but no more than 57% of the vote

b. It is estimated that the percentage that will vote for Candidate Jones is somewhere between 52% and 57%, based upon a method that will yield a correct estimate 95 times out of 100.

c. Candidate Jones can be expected to win with at least 52% of the vote.

d. All of these are correct interpretations

b. It is estimated that the percentage that will vote for Candidate Jones is somewhere between 52% and 57%, based upon a method that will yield a correct estimate 95 times out of 100.