WSU 311 TEST 2

18. The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making more than five errors. A) .29 B) .43 C) .57 D) .71

A

21. The following distribution most closely approximates a There is a graph A) normal distribution B) positively skewed distribution C) negatively skewed distribution D) multimodal distribution

A

25. The normal distribution is symmetrical, which means that A) scores above the mean are distributed the same as scores below the mean B) extreme scores are possible in a normal distribution C) there are an infinite number of possible normal distributions D) this characteristic has no practical implication

A

26. The standard normal distribution is normally distributed with a mean of ____ and a variance of ____. A) 0; 1 B) 1; 0 C) any value; any positive value D) any positive value; any value

A

3. Two outcomes are said to be mutually exclusive when A) the probability of the two outcomes occurring together is equal to zero (p = 0) B) the probability of the occurrence of one outcome has no effect on the probability of the occurrence of the second outcome C) the probability of the two outcomes occurring together is greater than zero (p > 0) D) the probability of the two outcomes occurring together sums to one

A

35. 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

38. 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

4. The proportion or fraction of times an outcome is likely to occur is referred to as A) Probability B) a random event C) sample space D) Luck

A

40. 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

44. 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

46. 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

1. Suppose that the probability that any child of alcoholic parents becomes alcoholic is p = .16. Assuming independent outcomes, the probability that two children of alcoholic parents will be alcoholic equals A) .16 B) .03 C) .25 D) .32

B

10. A researcher reports that the probability of a college student living on campus is p = .38. If a small local college has 2,000 students enrolled, then what is the standard deviation of college students living on campus? Hint: This is a binomial probability distribution. A) 471.2 students B) 21.7 students C) 760 students D) There is not enough information to answer this question.

B

11. A researcher determines that the probability of missing class among students at a local school is p = .16. Assuming that the school has 300 students enrolled, how many students can we expect to miss class on a given day? Hint: This is a binomial probability distribution. A) 252 students B) 48 students C) 16 students D) There is not enough information to answer this question.

B

15. The probability of a college student being employed is p = .35. The probability of a student being employed and dropping out of college is p = .20. Hence, the probability of a student dropping out of college, given that he or she is employed, is A) p = .07 B) p = .57 C) p = .55 D) There is not enough information to answer this question.

B

20. The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at most two errors. A) .29 B) .43 C) .57 D) .71

B

23. What is the implication for the tails of a normal distribution being asymptotic? A) that scores above the mean are distributed the same as scores below the mean B) that extreme scores are possible in a normal distribution C) that there are an infinite number of possible normal distributions D) that this characteristic has no practical implication

B

28. A researcher wants to know the probability of being named on the honor roll from a population where 8% of students are on the honor roll. If the researcher selects a sample of 400 students, then what is the mean number of students expected to be on the honor roll? Hint: This is a binomial distribution, where p = 0.08 and q = 0.92. A) 29 B) 32 C) 368 D) 200

B

29. What is the z score for scores in the bottom 5%? A) 1.645 B) -1.645 C) .4801 D) -0.050

B

31. Which proportion is largest in a z distribution? A) The proportion of area above the mean. B) The proportion of area between z = +1 and z = -1. C) The proportion of area greater than z = 1.0. D) The proportion of area less than z = 0.

B

32. Scores far from the mean are located in the ________ of a normal distribution. A) Body B) Tails C) most sensitive areas D) most uncertain areas

B

33. What is the z score for scores in the top 2.5%? A) .675 B) 1.96 C) .0124 D) .0250

B

36. Each of the following statements are true, except that 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

37. 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

42. 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

5. A therapist goes through her records and finds that 200 of her 400 patients showed significant improvement in mental health over the past year. Hence, the probability of her patients showing significant improvement in mental health is A) .05 B) .50 C) 200 D) 400

B

51. EXTRA CREDIT!! 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

9. Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities? A) additive rule B) multiplicative rule C) both A and B D) none of the above

B

13. If the standard deviation of a probability distribution is 9, then the variance is A) 3 B) 9 C) 81 D) unknown

C

16. Bayes' theorem is often applied to a variety of ________ probability situations, including those related to statistical inference. A) generic B) absolute C) conditional D) Fixed

C

19. The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at least three errors. A) .29 B) .43 C) .57 D) .71

C

2. In a factory that makes widgets, defective widgets are sometimes made. The probability of 0-2 defective widgets per 1000 widgets is .51. The probability of 3-5 defective widgets per 1000 is .24. What is the probability of more than 5 defective widgets? A) .75 B) .49 C) .25 D) 0

C

22. The normal distribution has all of the following characteristics, except A) the mean can be any number B) it is mathematically defined C) the total area under the curve is greater than 1.0 D) the mean, median, and mode are equal

C

24. An example of a binomial variable includes A) time (in seconds) B) weight (in pounds) C) sex (male, female) D) all of the above

C

30. State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the left of z = 0.80, or the area to the right of z = -0.80. A) The first area is bigger. B) The second area is bigger. C) The two areas are the same.

C

34. A normal distribution has a mean equal to 53. What is the standard deviation of this normal distribution if 2.5% of the proportion under the curve lies to the right of x = 66.72? (Round your answer to two decimal places) A) -7.00 B) 0.14 C) 7.00 D) 49.00

C

39. 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

43. 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

45. 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

50. How many possible samples of size 2 can be selected from a population of 5 using theoretical sampling? A) 5 B) 10 C) 25 D) 32

C

8. In a game, the probability of winning money is p = .16, the probability of losing money is p = .54, and the probability of breaking even is p = .30. What is the probability of winning or losing money in this game? A) .16 B) .54 C) .70 D) 1.00

C

For the experimental sampling strategy, A) the order in which a participant is selected matters B) sampling is with replacement C) sampling is without replacement D) participants are not sampled from the population, but instead are sampled from other samples already drawn

C

12. Each of the following is an example of a binomial distribution, except A) the number of heads in ten flips of a fair coin B) the number of males and females in a sample C) the number of votes for or against a candidate D) the time it takes to complete a driving test

D

14. When the probability of one outcome changes depending on the occurrence of a second outcome, these outcomes are referred to as A) mutually exclusive B) complementary C) independent D) conditional

D

17. The probability of making zero to two errors per 1,000 keystrokes is 0.43, and the probability of making three to five errors per 1,000 keystrokes is 0.28. Find the probability (per 1,000 keystrokes) associated with making at most five errors. A) .29 B) .43 C) .57 D) .71

D

27. The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a A) standardized score B) x-score C) normalized deviation D) z score

D

47. 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

48. Increasing the number of observations or samples in a study will decrease the standard error (standard error of the mean). This is known as A) Bob (not the right answer) B) the law of diminishing returns C) the theoretical law of estimates D) the law of large numbers

D

49. 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 - 1 D) both B and C

D

52. EXTRA CREDIT!! 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

6. A researcher records the following data for the number of bids made on a sample of items sold at an auction. Based on the table, what was the probability that an item had 7 bids made on it? Number of Bids Frequencies 3 5 4 12 5 7 6 6 7 10 A) 5 B) 10 C) .10 D) .25

D

7. Which of the following is NOT a characteristic of probability? A) Probability varies between 0 and 1. B) Probability can never be negative. C) Probability can be stated as a fraction or decimal. D) Probability is most useful for describing fixed events.

D