Statistics chapter 6

How is the standard error of the mean typically reported in a graph? a. by plotting sample means b. using error bars c. by listing group names along the x-axis d. it is never reported in a graph

b. using error bars

The mean of the sampling distribution of sample means is ______. a. equal to the population mean b. equal to the population variance c. both A and B d. none of these

a. equal to the population mean

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5. What is the probability of selecting a sample mean that is at least two standard deviations larger than the population mean? a. .0228 b. equal to the probability of selecting a sample mean that is at least two standard deviations below the mean c. .9772 d. .4772

a. .0228

A researcher selects a sample of 9 participants from a population with a mean of 8 and a standard deviation of 3. About 14% of the sample means in this sampling distribution should be between a sample mean of ______. a. 9 and 10 b. 5 and 6 c. 10 and 11 d. 6 and 8

a. 9 and 10

A researcher selects two samples of 25 participants each. In the first sample, the population mean was 32 and the variance was 8. In this second sample, the population mean was 4 and the variance was 8. Which sample will be associated with a larger standard error of the mean? a. None, both samples will have the same value for standard error b. Sample 1 c. Sample 2 d. There is not enough information to answer this question.

a. None, both samples will have the same value for standard error

The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean? Researcher A: n = 18, mu = 8, sigma = 2.4 Researcher B: n = 12, mu = 8, sigma = 2.4 a. Researcher A b. Researcher B c. They both have the same standard error.

a. Researcher A

A sampling distribution of the sample mean or variance is ______. a. a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population b. a distribution of all scores that could be obtained in samples of a given size from one or more populations c. a distribution of all measures that could be obtained in a given sample of a given size d. a distribution of all scores that could be obtained in a population

a. a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population

It happens to be the case that the standard error of the sampling distribution of sample means ______. a. is minimal b. is approximately equal to that in the population c. both A and C d. gets larger as the sample size increases

a. is minimal

A researcher randomly selects a sample of participants from a population with a variance of 4. If a researcher selects a sample of 16 participants with a mean of 12, then what is the mean and standard error for the sampling distribution of the mean? a. mean = 12, standard error = 0.5 b. mean = 12, standard error = 1 c. mean = 12, standard error = 2 d. There is not enough information to answer this question.

a. mean = 12, standard error = 0.5

Which of the following allows researchers to use the standard normal distribution to estimate the probability of selecting sample means? a. the central limit theorem b. the fact that increasing sample size will decrease standard error c. the fact that sample means vary minimally from the population mean d. the skewed distribution rule

a. the central limit theorem

A researcher selects a sample of 64 participants from a population with a mean of 10 and a variance of 16. What is the standard error of the mean? a. 10 b. 0.5 c. 2.0 d. There is not enough information to answer this question.

b. 0.5

A researcher selects a sample of size 6 from a population of size 10. How many possible samples of this size can be selected using theoretical sampling? a. 10,000,000 b. 1,000,000 c. 100,000 d. over 60,000,000 samples

b. 1,000,000

What is the central limit theorem? a. It explains that sample means will vary minimally from the population mean. b. It explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population. c. It explains that if we select a sample at random, then on average we can expect the sample mean to equal the population mean. d. all of these

b. It explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population.

A researcher selects two samples of 64 participants each. In the first sample, the population mean was 10 and the variance was 16. In this second sample, the population mean was 25 and the variance was 9. Which sample will be associated with a larger standard error of the mean? a. None, both samples will have the same value for standard error. b. Sample 1 c. There is not enough information to answer this question. d. Sample 2

b. Sample 1

The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean? Researcher A: n = 25, mu= 5, sigma = 7 Researcher B: n = 25, mu = 32, sigma = 7 a. Researcher B b. They both have the same standard error. c. Researcher A

b. They both have the same standard error.

Regardless of the distribution of the population, the sampling distribution of sample means will be approximately normally distributed. What characteristic of the mean explains this? a. unbiased estimator b. central limit theorem c. minimal variance d. none of these

b. central limit theorem

A researcher increases the sample size, which will ______. a. reduce variability in the population b. decrease the value of standard error c. increase the value of standard error d. increase variability in the population

b. decrease the value of standard error

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean of 13 or larger from this population? a. about one standard deviation below the mean b. less than .03 c. greater than .31 d. equal to the probability of selecting a score above the mean

b. less than .03

A researcher selects from a participant pool of four males and six females. He determines that the probability of selecting two male participants is p = .16. Based on this probability, what strategy did the researcher use to sample participants? a. sampling without replacement b. sampling with replacement

b. sampling with replacement

A researcher selects from a participant pool of four males and six females. He determines that the probability of selecting two female participants is p = .30. Based on this probability, what strategy did the researcher use to sample participants? a. sampling with replacement b. sampling without replacement

b. sampling without replacement

Experimental research is typically conducted using a sampling strategy in which ______. a. the order of selecting participants matters b. the same participant can never be selected twice in the same sample c. participants are replaced after being sampled d. all of these

b. the same participant can never be selected twice in the same sample

What does it mean to say that the sample mean is an unbiased estimator of the population mean? a. The sample means will vary minimally from the population mean. b. The sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population. c. If we select a sample at random, then on average we can expect the sample mean to equal the population mean. d. all of these

c. If we select a sample at random, then on average we can expect the sample mean to equal the population mean.

The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean? Researcher A: n = 36, mu = 12, sigma = 9 Researcher B: n = 36, mu = 12, sigma = 6 a. They both have the same standard error. b. Researcher A c. Researcher B

c. Researcher B

Two researchers select a sample for a population with a mean of 12.4 and a standard deviation of 9. Researcher A selects a sample of 30 participants. Researcher B selects a sample of 40 participants. Which sample is associated with a smaller standard error? a. Researcher B's, because the sample size was smaller. b. Researcher A's, because the sample size was larger. c. Researcher B's, because the sample size was larger. d. Researcher A's, because the sample size was smaller.

c. Researcher B's, because the sample size was larger.

A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called ______. a. a conditional procedure b. random sampling c. a sampling distribution d. sampling without replacement

c. a sampling distribution

A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean that is at least equal to the population mean? a. .50 b. equal to the probability of selecting a sample mean that is at most equal to the population mean c. both A and B d. none of these

c. both A and B

A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5. What is the probability of selecting a sample mean equal to at least 12? a. greater than 50% b. about the same as selecting a sample mean that is at least equal to the population mean c. equal to the probability of selecting a sample mean that is at most equal to 8 d. less than 1%

c. equal to the probability of selecting a sample mean that is at most equal to 8

Suppose you select a sample of three people from a population of four (A, B, C, D). Which of the following samples is possible using the experimental sampling strategy? a. persons A, D, and D b. persons A, C, and A c. persons B, C, and D d. persons B, A, and B

c. persons B, C, and D

Each of the following statements are true, except that ______. a. the larger the standard deviation in the population, the larger the standard error b. the smaller the sample size, the larger the population size c. the larger the sample size, the larger the standard error d. increasing the sample size will decrease standard error

c. the larger the sample size, the larger the standard error

A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20. About 68% of the sample means in this sampling distribution should be between a sample mean of ______. a. 34 and 38 b. 38 and 44 c. 18 and 58 d. 36 and 40

d. 36 and 40

A researcher selects a sample of size 4 from a population of size 6. How many possible samples of this size can be selected using experimental sampling? a. 1,296 b. 4,096 c. 30 d. 15

d. 15

A researcher randomly selects a sample of athletes and reports that their average score on a health and fitness scale is 23. Based on the characteristics of the sample mean, what does this say about the mean in the population? a. It tells us that the mean in the population is no less than 23. b. There is no way to know without knowing the size of the sample. c. Nothing; it was just a sample. d. We expect that the population mean is equal to 23 because the sample mean is an unbiased estimator of the population mean.

d. We expect that the population mean is equal to 23 because the sample mean is an unbiased estimator of the population mean.

Because the sampling distribution of sample means is normally distributed, we can use the z transformation formula to find probabilities. Which of the following gives the appropriate notation for this formula? a. mc030-1.jpg b. mc030-2.jpg c. mc030-3.jpg d. all of these

d. all of these

In terms of characterizing samples, statistical theory was developed using a sampling strategy in which ______. a. the order of selecting participants matters b. the same participant can be selected twice in the same sample c. participants are replaced after being sampled d. all of these

d. all of these

As sample size increases, the standard error of the mean ______. a. increases b. does not change c. can increase or decrease d. decreases

d. decreases

Which type of sampling is most often applied by researchers in the behavioral sciences? a. standard normal sampling b. theoretical sampling c. normal sampling d. experimental sampling

d. experimental sampling

The shape of the sampling distribution of the mean is approximately ______, whereas the shape of the sampling distribution of the variance is approximately ______. a. normal; normal b. positively skewed; normal c. positively skewed; positively skewed d. normal; positively skewed

d. normal; positively skewed

A researcher selects a sample of 121 participants from a population with a mean of 32 and a standard deviation of 22. What is the standard error of the mean? a. 2.0 b. 32 c. There is not enough information to answer this question. d. 0.5

a. 2.0

A researcher states that a sample of 100 shoppers spend 112 ± 40 (M ± SEM) dollars on groceries each week. Which value is the standard error of the mean? a. 112 b. 100 c. The standard error of the mean is not reported in the article. d. 40

d. 40

An article states that a sample of 40 participants took 12 ± 2.3 (M ± SEM) s to complete a cognitive assessment. Which value is the standard error of the mean? a. 12 b. 40 c. 2.3 d. The standard error of the mean is not reported in the article.

c. 2.3

What values are distributed along the x-axis for a sampling distribution of the sample variance? a. both B and C b. scores c. sample means d. sample variances

d. sample variances

What values are distributed along the x-axis for a sampling distribution of the sample mean? a. both B and C b. scores c. sample variances d. sample means

d. sample means

The sampling distribution of the mean and the sampling distribution of the variance (when dividing SS by n - 1) ______. a. are both unbiased estimators b. both follow the central limit theorem c. are both associated with minimal variance d. all of these

a. are both unbiased estimators