data analysis ch. 7 study guide

23. 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) 32 B) 2.0 C) 0.5 D) There is not enough information to answer this question.

B) 2.0

50. 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) 40 C) 100 D) The standard error of the mean is not reported in the article

B) 40

30. In terms of estimating the population variance, what is one disadvantage for dividing SS by df to calculate sample variance? A) It is an unbiased estimator. B) It does not have minimum variance. C) It underestimates the population variance on average. D) None; there are no disadvantages for dividing SS by df to calculate sample variance.

B) It does not have minimum variance.

43. 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 the above

C) both A and B

12. Which type of sampling is most often applied by researchers in the behavioral sciences? A) theoretical sampling B) normal sampling C) experimental sampling D) standard normal sampling

C) experimental sampling

42. 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) equal to the probability of selecting a score above the mean B) about one standard deviation below the mean C) less than .03 D) greater than .31

C) less than .03

10. 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) 100,000 B) 1,000,000 C) 10,000,000 D) over 60,000,000 samples

B) 1,000,000

45. 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) less than 1% B) greater than 50% C) about the same as selecting a sample mean that is at least equal to the population mean D) equal to the probability of selecting a sample mean that is smaller than 8

D) equal to the probability of selecting a sample mean that is smaller than 8

6. A researcher selects from a participant pool of 4 males and 6 females. He determines that the probability of selecting 2 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

32. What characteristic of the sample variance do researchers generally consider more important: unbiased estimator or minimum variance? A) minimum variance B) unbiased estimator C) Neither one; they are equally important.

B) unbiased estimator

22. 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) 2.0 C) 0.5 D) There is not enough information to answer this question.

C) 0.5

49. An articles states that a sample of 40 participants took 12 ± 2.3 (M ± SEM) seconds to complete a cognitive assessment. Which value is the standard error of the mean? A) 40 B) 12 C) 2.3 D) The standard error of the mean is not reported in the article

C) 2.3

47. 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) 6 and 8 B) 5 and 6 C) 9 and 10 D) 10 and 11

C) 9 and 10

44. 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) .4772 C) .9772 D) equal to the probability of selecting a sample mean that is at least two standard deviations below the mean

A) .0228

11. 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) 15 B) 30 C) 1,296 D) 4,096

A) 15

9. 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, C, and A B) persons A, D, and D C) persons B, C, and D D) persons B, A, and B

C) persons B, C, and D

36. 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

24. 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) Sample 1 B) Sample 2 C) None, both samples will have the same value for standard error D) There is not enough information to answer this question.

A) Sample 1

28. Suppose that a researcher selects a sample of participants from a population. If the shape of the distribution in this population is negatively skewed, then what is the shape of the sampling distribution of sample variances? A) approximately positively skewed B) approximately negatively skewed C) approximately normally distributed D) There is not enough information to answer this question, because the population mean and variance are not given.

A) approximately positively skewed

19. 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 the above

A) are both unbiased estimators

21. 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 the above

A) equal to the population mean

15. 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) gets larger as the sample size increases D) both A and C

A) is minimal

27. A researcher selects a sample of 16 participants from a population with a variance of 4. What is the standard error of the mean? A) less than 1 B) equal to 1 C) greater than 1 D) There is not enough information to answer this question.

A) less than 1

5. A researcher selects from a participant pool of 4 males and 6 females. He determines that the probability of selecting 2 male participants is p = .16. Based on this probability, what strategy did the researcher use to sample participants. A) sampling with replacement B) sampling without replacement

A) sampling with replacement

39. 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 skewed distribution rule C) the fact that sample means vary minimally from the population mean D) the fact that increasing sample size will decrease standard error

A) the central limit theorem

48. How is the standard error of the mean typically reported in a graph? A) using error bars B) by plotting sample means C) by listing group names along the x-axis D) it is never reported in a graph

A) using error bars

14. 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 the above

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.

35. 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 (pg 541) A) Researcher A B) Researcher B C) They both have the same standard error.

B) Researcher B

1. 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) a sampling distribution C) sampling without replacement D) random sampling

B) a sampling distribution

16. 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 the above

B) central limit theorem

40. A researcher increases the sample size, which will: A) increase the value of standard error B) decrease the value of standard error C) reduce variability in the population D) increase variability in the population

B) decrease the value of standard error

34. As sample size increases, the standard error of the mean (pg. 541) A) increases B) decreases C) can increase or decrease D) does not change

B) decreases

31. Regardless of the shape of the distribution in the population, the sampling distribution of sample variances approximates a A) normal distribution B) positively skewed distribution C) negatively skewed distribution D) multimodal distribution

B) positively skewed distribution

2. What values are distributed along the x-axis for a sampling distribution of the sample mean? A) scores B) sample means C) sample variances D) both B and C

B) sample means

38. Each of the following statements are true, except that (pg. 541) A) increasing the sample size will decrease standard error B) the larger the sample size, the larger the standard error C) the larger the standard deviation in the population, the larger the standard error D) both B and C

B) the larger the sample size, the larger the standard error

8. 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 the above

B) the same participant can never be selected twice in the same sample

13. 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 the above

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

25. 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) Sample 1 B) Sample 2 C) None, both samples will have the same value for standard error D) There is not enough information to answer this question.

C) None, both samples will have the same value for standard error

37. 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 A B) Researcher B C) They both have the same standard error.

C) They both have the same standard error.

26. Suppose that a researcher selects a sample of participants from a population. If the shape of the distribution in this population is positively skewed, then what is the shape of the sampling distribution of sample means? A) approximately positively skewed B) approximately negatively skewed C) approximately normally distributed D) There is not enough information to answer this question, because the population mean and variance are not given.

C) approximately normally distributed

20. 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 = 2 B) mean = 12, standard error = 1 C) mean = 12, standard error = 0.5 D) There is not enough information to answer this question.

C) mean = 12, standard error = 0.5

18. 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) normal; positively skewed D) positively skewed; positively skewed

C) normal; positively skewed

3. What values are distributed along the x-axis for a sampling distribution of the sample variance? A) scores B) sample means C) sample variances D) both B and C

C) sample variances

46. 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 40 B) 34 and 38 C) 38 and 44 D) 36 and 40

D) 36 and 40

33. 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? (pg. 541) A) Researcher A's, because the sample size was smaller. B) Researcher B's, because the sample size was smaller. C) Researcher A's, because the sample size was larger. D) Researcher B's, because the sample size was larger.

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

17. 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) Nothing; it was just a sample. B) There is no way to know without knowing the size of the sample. C) It tells us that the mean in the population is no less than 23. 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.

4. A sampling distribution of the sample mean or variance is A) a distribution of all measures that could be obtained in a given sample of a given size 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 scores that could be obtained in a population D) a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population

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

***41. 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) B) C) D) all of the above

D) all of the above

7. 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 the above

D) all of the above

29. The sample variance is an unbiased estimator of the population variance A) when dividing SS by n B) when dividing SS by df C) when dividing SS by n ñ 1 D) both B and C

D) both B and C