Probability and Sampling, Intro to Hypothesis Testing, Exams of Nursing

Download Probability and Sampling, Intro to Hypothesis Testing and more Exams Nursing in PDF only on Docsity! Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, (228 Terms) with Correct Solutions 2023- 2034. 1. Which of the following are requirements of a random sample? a. Every individual has an equal chance of being selected. b. The probabilities cannot change during a series of selections. c. There must be sampling with replacement. d. There must be at least 100 observations. - Answer: A 2. A jar contains 10 red marbles and 30 blue marbles. What is the probability of randomly selecting a red marble from the jar? a. 10/30 b. 10/40 c. 1/10 d. 1/40 - Answer: B 3. A jar contains 10 red marbles and 30 blue marbles. A random sample without replacement of n=3 marbles is Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, selected from the jar. If the first two marbles are both blue, what is the probability that the third marble will be red? a. 10/37 b. 10/38 c. 10/40 d. 8/38 - Answer: B 4. What proportion of a normal distribution is located in the tail below z=2.00? a. 0.9772 b. 0.0228 c. 0.4772 d. 0.0456 - Answer: B 5. What proportion of a normal distribution is located in the tail beyond z=-1.00? a. 0.8413 b. 0.1587 c. 0.3413 d. 0.1587 - Answer: B Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, c. 0.0987 d. 0.1974 - Answer: D 12. What proportion of a normal distribution is located between z=-1.50 and z= +1.50? a. 0.9332 b. 0.0668 c. 0.4332 d. 0.8664 - Answer: D 13. What is the probability of randomly selecting a z-score greater than z=0.75 from a normal distribution? a. 0.7734 b. 0.2266 c. 0.2734 d. 0.4532 - Answer: B 14. What is the probability of randomly selecting a z-score less than z=1.25 from a normal distribution. a. 0.8944 b. 0.1056 Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, c. 0.3944 d. 0.2112 - Answer: A 15. What z-score value separates the top 10% of a normal distribution from the bottom 90%? a. z= 1.28 b. z=0.25 c. Z=-1.28 d. z=-0.25 - Answer: A 16. What z-score value separates the top 70% of a normal distribution from the bottom 30%? a. z=0.52 b. z=0.84 c. Z=-0.52 d. z=-0.84 - Answer: C 17. What z-score values form the boundaries for the middle 60% of a normal distribution? a. z=+0.25 and z=-0.25 b. z=+0.39 and z=-0.39 Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, c. z=+0.52 and z=-0.52 d. z= +0.84 and z=-0.84 - Answer: D 18. A normal distribution has a mean of u = 40 with o=10. What proportion of the scores in this distribution is greater than X= 55? a. 0.3085 b. 0.6915 c. 0.0668 d. 0.9332 - Answer: C 19. A normal distribution has a mean of u = 40 with o= 10. What proportion of the scores in this distribution are smaller than X = 35? a. 0.3085 b. 0.6915 c. 0.0668 d. 0.9332 - Answer: A 20. A normal distribution has u = 80 and o= 10. What is the probability of randomly selecting a score greater than 90 Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, a. 0.8413 b. 0.1587 c. 0.3413 d. 0.6826 - Answer: C 26. A normal distribution has a mean of u = 100 with o = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 90 and X = 110? a. 0.6915 b. 0.3085 c. 0.1915 d. 0.3830 - Answer: D 27. A normal distribution has a mean of u = 100 with o = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 90 and X = 120? a. 0.1498 b. 0.4672 c. 0.5328 Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, d. 0.2996 - Answer: C 28. A normal distribution has a mean of u = 80 with o = 20. What score separates the highest 15% of the distribution from the rest of the scores? a. X= 59.2 b. X= 100.8 c. X=95 d. X = 65 - Answer: B 29. A normal distribution has a mean of u = 80 with o=20. What score separates the highest 40% of the distribution from the rest of the scores? a. X= 75 b. X=85 c. X= 54.4 d. X= 105.6 - Answer: B 30. A normal distribution has a mean of u = 80 with o=20. What score separates the lowest 30% of the distribution from the rest of the scores? Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, a. X=90.4 b. X= 69.6 c. X=110 d. X = 50 - Answer: B 31. A normal distribution has a mean of u = 24 with o=3. What is the minimum score needed to be in the top 14% of the distribution? a. X= 20.76 b. X = 27.24 c. X=25.08 d. X= 24.42 - Answer: B 32. Scores on the SAT form a normal distribution with a mean of u = 500 with o= 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted? a. X=475 b. X= 525 c. X=440 d. X= 560 - Answer: A Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 38. A multiple-choice test with 48 questions has four choices for each question. What is the probability of getting more than 12 questions correct by just guessing? a. 0.5000 b. 0.4325 c. 0.5675 d. 0.0675 - Answer: B 39. A true/false test has 100 questions. Using the normal approximation to the binomial distribution, what is the probability of getting 55 or more correct by just guessing? a. p(X> 55) b. p(X> 55.5) c. p(X > 54.5) d. p(X> 45) - Answer: C 40. A true/false test has 100 questions. Using the normal approximation to the binomial distribution, what is the probability of getting more than 55 correct by just guessing? a. p(X> 55) Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, b. p(X> 55.5) c. p(X> 54.5) d. p(X> 45) - Answer: B 41. All probabilities can be expressed as decimal values ranging from 0 to 1.00. a. True b. False - Answer: T 42. A jar contains 10 red marbles and 20 blue marbles. If you take a random sample with the replacement of two marbles from this jar and the first marble is blue, then the probability that the second marble is blue is p= 19/29. a. True b. False - Answer: F 43. For a normal distribution, proportions in the right-hand tail are positive and proportions in the left-hand tail are negative. a. True b. False - Answer: F 44. A vertical line drawn through a normal distribution at z= 1.25 will separate the distribution into two sections. The proportion in the smaller section is 0.1056. a. True b. False - Answer: T Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 45. A vertical line drawn through a normal distribution at z=-0.75 will separate the distribution into two sections. The proportion in the smaller section is 0.2734. a. True b. False - Answer: F 46. A vertical line drawn through a normal distribution at z=-0.80 will separate the distribution into two sections. The proportion in the larger section is 7881. a. True b. False - Answer: T 47. When the Z-score value in a normal distribution is negative, the majority of the area is on the right-hand side of the distribution a. True b. False - Answer: T 48. For any normal distribution, the proportion in the tail above z=2.00 is p=0.0228. a. True b. False - Answer: T 49. For a normal distribution, the proportion in the tail below z=-2.00 is equal to 0.0228. a. True b. False - Answer: T Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 60. If one score is randomly selected from a normal distribution with u = 100 and o= 20, the probability of obtaining a score less than X = 95 is p=0.4013. a. True b. False - Answer: T 61. If one score is randomly selected from a normal distribution with u = 100 and o=20, the probability of obtaining a score less than X = 70 is p=0.0013. a. True b. False - Answer: F 62. If one score is randomly selected from a normal distribution with u = 100 and o=20, the probability of obtaining a score between X = 90 and X = 100 is p=0.3085. a. True b. False - Answer: F 63. If one score is randomly selected from a normal distribution with u = 100 and 6 = 20, the probability of obtaining a score between X = 80 and X = 120 is p=0.3413. a. True b. False - Answer: F 64. A binomial distribution with p=2/3 and n= 24 meets the criterion for using the normal approximation. a. True b. False - Answer: F Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 65. The binomial distribution for p= 1/4 and n=96 has a mean of u = 24. a. True b. False - Answer: T 66. The binomial distribution for p= 1/2 and n= 100 has a standard deviation of o = 25. a. True b. False - Answer: F 67. For a binomial distribution, the probability of obtaining a score greater than 19 is computed as p(X> 19.5). a. True b. False - Answer: T 68. For a binomial distribution, the probability of obtaining a score of X = 19 or greater is computed as p(X> 18.5). a. True b. False - Answer: T 69. For the normal approximation to the binomial distribution with n= 100 and p= 1/2; a score of X = 60 corresponds to a Z-score of z=2.00. a. True b. False - Answer: T Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 70. For the normal approximation to the binomial distribution with n=100 and p=1/5, the probability of selecting a score greater than or equal to 25 is p=0.1056. a. True b. False - Answer: F 71. Assume that a vertical line is drawn through a normal distribution at each of the following z-score locations. In each case, determine whether the tail is on the left side or the right side of the line and find the proportion of the distribution that is located in the tail. a. z= +1.80 b. z= +0.60 c. Z=-0.40 d. z=-1.25 - Answer: ANSWER: : a. The tail is on the right. p=0.0359 b. The tail is on the right. p=0.2743 c. The tail is on the left. p=0.3446 d. The tail is on the left. p=0.1056 72. For a normal distribution, a. What z-score separates the highest 10% from the rest of the scores? b. What z-score separates the highest 30% from the rest of the scores? c. What z-score separates the lowest 40% from the rest of the scores? Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, a. What is the probability that a subject would guess exactly 18 correct in a series of 36 trials? b. What is the probability that a subject would guess more than 20 correct in a series of 36 trials? - Answer: ANSWER: : a. With n= 36 and p=q= 1/2, you may use the normal approximation with u = 18 and o=3. X= 18 has real limits of 17.5 and 18.5 corresponding to z=0.17 and z=+0.17.p=0.1350. b. p(X> 20.5) =p(z>0.83) 1. What term is used to identify the mean of the distribution of sample means? a. the expected value of M b. the standard error of M c. the sample mean d. the central limit mean - Answer: A 2. What term is used to identify the standard deviation of the distribution of sample means? a. the expected value of M b. the standard error of M Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, c. the sample mean d. the central limit mean - Answer: B 3. For a population with u = 80 and o=20, the distribution of sample means based on n= 16 will have an expected value of_ and a standard error of a. 5; 80 b. 80; 5 c. 20; 20 d. 80; 1.25 - Answer: B 4. The distribution of sample means a. is always a normal distribution b. will be normal only if the population distribution is normal c. will be normal only if the sample size is at least n= 30 d. will be normal if either the population is normal or the sample size is n > 30 - Answer: D 5. A sample of n= 100 scores is selected from a population with u = 80 with o= 20. On average, how much error is expected between the sample mean and the population mean? Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, a. 0.2 points b. 0.8 points c. 2 points d. 4 points - Answer: C 6. A sample of n= 16 scores is selected from a population with u = 80 with o = 20. On average, how much error would be expected between the sample mean and the population mean? a. 20 points b. 5 points c. 4 points d. 1.25 points - Answer: B 7. What symbol is used to identify the standard error of M? a. OM b. u c. σ/ d. MM - Answer: C 8. Under what circumstances is the distribution of the sample means normal? Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 13. If random samples, each with n=9 scores, are selected from a normal population with u = 80 and o= 36, then what is the expected value of the mean of the distribution of sample means? a. 4 b. 12 c. 16 d. 80 - Answer: D 14. If random samples, each with n=4 scores, are selected from a normal population with u = 80 and 6 = 36, then what is the standard error for the distribution of sample means? a. 4 b. 9 c. 18 d. 36 - Answer: C 15. If all the possible random samples with n = 36 scores are selected from a normal population with u = 80 and o=18, and the mean is calculated for each sample, then what is the average of all the sample means? a. 2 Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, b. 6 c. 80 d. It cannot be determined without additional information. - Answer: C 16. If random samples, each with n= 36 scores, are selected from a normal population with u = 80 and o= 18, how much difference, on average, should there be between a sample mean and the population mean? a. 2 points b. 3 points c. 6 points d. 18 points - Answer: B 17. What happens to the expected value of M as sample size increases? a. It also increases. b. It decreases. c. It stays constant. d. The expected value does not change in a predictable manner when sample size increases. - Answer: C 18. What happens to the standard error of M as sample size increases? Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, a. It also increases. b. It decreases. c. It stays constant. d. The standard error does not change in a predictable manner when sample size increases. - Answer: B 19. Which combination of factors will produce the smallest value for the standard error? a. A large sample and a large standard deviation b. A small sample and a large standard deviation c. A large sample and a small standard deviation d. A small sample and a small standard deviation - Answer: C 20. For a particular population, a sample of n=9 scores has a standard error of 8. For the same population, a sample of n = 16 scores would have a standard error of_ . a. 8 b. 6 c. 4 - Answer: B Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 28. A sample of n= 16 scores is obtained from a population with u = 50 and o= 16. If the sample mean is M= 54, then what is the z-score for the sample mean? a. z=0.25 b. z=0.50 c. z=1.00 d. z= 4.00 ANSWER: : C - Answer: C 29. A sample of n=9 scores is obtained from a population with u = 70 and 5= 18. If the sample mean is M = 76, then what is the z-score for the sample mean? a. z=0.33 b. z=0.50 c. z=1.00 d. z=3.00 ANSWER: : c - Answer: C 30. If a sample of n = 4 scores is obtained from a population with u = 70 and o = 12, then what is the Z-score corresponding to a sample mean of M = 76? a. z=0.25 b. z=0.50 c. z=1.00 d. z=2.00 ANSWER: : C - Answer: C 31. A sample of n= 4 scores is obtained from a population with u = 70 and o=8. If the sample mean corresponds to a z Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, score of 2.00, then what is the value of the sample mean? a. M= 86 b. M= 78 c. M= 74 d. M= 72 ANSWER: : b - Answer: B 32. A sample from a population with u = 40 and o= 10 has a mean of M= 44. If the sample mean corresponds to a z= 2.00, then how many scores are in the sample? a. n= 100 b. n=25 c. n=5 d. n=4 ANSWER: : b - Answer: B 33. A random sample of n= 16 scores is obtained from a population with o= 12. If the sample mean is 6 points greater than the population mean, what is the z-score for the sample mean? a. +6.00 b. +2.00 c. +1.00 d. It cannot be determined without knowing the population mean. ANSWER: : b - Answer: B 34. For a normal population with u = 40 and o= 10 which of the following samples is least likely to be obtained? a. M=42 for a sample of n=4 b. M = 44 for a sample of n=4 c. M=42 for a sample of n= 100 d. M=44 for a sample of n= 100 Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, ANSWER: : a - Answer: A 35. For a normal population with u = 40 and o= 10 which of the following samples has the highest probability of being obtained? a. M = 42 for a sample of n= 4 b. M = 44 for a sample of n = 4 c. M=42 for a sample of n=100 d. M = 44 for a sample of n= 100 ANSWER: : d - Answer: D 36. A random sample of n= 4 scores is obtained from a normal population with u = 20 and o = 4. What is the probability that the sample mean will be greater than M = 22? a. 0.50 b. 1.00 c. 0.1587 d. 0.3085 ANSWER: : c - Answer: C 37. A random sample of n=9 scores is obtained from a normal population with u = 40 and o= 6. What is the probability that the sample mean will be greater than M=43? a. 0.3085 b. 0.6915 c. 0.9332 d. 0.0668 ANSWER: : d - Answer: D Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 46. As the sample size increases, the standard error also increases. a. True b. False ANSWER: : False - Answer: F 47. The mean for a sample of n = 4 scores has a standard error om = 5 points. This sample was selected from a population with a standard deviation of o=20. a. True b. False ANSWER: : False - Answer: F 48. If samples are selected from a normal population, the distribution of sample means will also be normal. a. True b. False ANSWER: : True - Answer: T 49. According to the central limit theorem, the standard error for a sample mean becomes smaller as the sample size increases. a. True b. False ANSWER: : True - Answer: T Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 50. If samples of size n= 16 are selected from a population with u = 40 and o=8, the distribution of sample means will have an expected value of 40. a. True b. False ANSWER: : True - Answer: T 51. If samples of size n= 16 are selected from a population with u = 40 and o=8, the distribution of sample means will have a standard error of 2 points. a. True b. False ANSWER: : True - Answer: T 52. A mathematical proposition known as the central limit theorem provides a precise description of the distribution that would be obtained if you selected every possible sample, calculated every sample mean, and constructed the distribution of the sample mean. a. True b. False ANSWER: : True - Answer: T 53. The mean for a sample of n=9 scores has a standard error of 2 points. This sample was selected from a population with a standard deviation of s = 18. a. True b. False ANSWER: : False - Answer: F Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 54. The law of large numbers states that the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean.. a. True b. False ANSWER: : True - Answer: T 55. If the standard deviation for a population increases, the standard error for sample means from the population will also increase. a. True b. False ANSWER: : True - Answer: T 56. The smallest possible standard error is obtained when a small sample is taken from a population with a small standard deviation. a. True b. False ANSWER: : False - Answer: F 57. On average, a sample of n= 16 scores from a population with s = 10 will provide a better estimate of the population mean than you would get with a sample of n= 16 scores from a population with s = 5. a. True b. False ANSWER: : False - Answer: F Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 65. A sample of n=9 scores is selected from a population with u = 50 and s = 12. The probability of obtaining a sample mean greater than 46 is p = 0.8413.Z - Answer: T 66. A sample of n=25 scores is selected from a population with u = 50 and o= 10. The probability of obtaining a sample mean greater than 55 is p=0.3085. - Answer: F 67. A sample of n= 16 scores is selected from a population with u = 70 and o= 8. It is very unlikely that the sample mean will be greater than 78. - Answer: T 68. A sample of n=25 scores is selected from a population with u = 70 and o= 20. It is very unlikely that the sample mean will be smaller than 72. a. True b. False - Answer: F 69. A population has u = 60 and 6 = 30. For a sample of n = 25 scores from this population, a sample mean of M=55 would be considered an extreme value. a. True b. False - Answer: F Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 70. A population has u = 60 and o= 10. For a sample of n=25 scores from this population, a sample mean of M= 55 would be considered an extreme value. a. True b. False - Answer: T 71. Define the distribution of sample means. - Answer: ANSWER: : The distribution of sample means is the set of sample means obtained from all the possible random samples of a specified size (n) taken from a particular population. 72. Describe what is measured by the standard error of M. - Answer: ANSWER: : The standard error of M is the standard deviation of the distribution of sample means, and provides a measure the expected distance (or deviation) on average between a sample mean M and the population mean u. 73. Describe the shape, the mean, and the standard deviation for each of the following two distributions. a. A population of scores with u = 50 and o=6. b. The distribution of sample means based on samples of n= 36 selected from a population with u = 50 and o=6. - Answer: ANSWER: : a. The population is a Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, distribution of scores with an unknown shape, a mean of u = 50 and a standard deviation of o=6. b. The distribution of sample means is approximately normal (because n > 30), with a mean (expected value) of u = 50, and a standard deviation (standard error) of OM=1. 74. A population has a mean of u = 80 with o = 20. a. If a single score is randomly selected from this population, how much distance, on average, should you find between the score and the population mean? b. If a sample of n=4 scores is randomly selected from this population, how much distance, on average, should you find between the sample mean and the population mean? c. If a sample of n= 100 scores is randomly selected from this population, how much distance, on average, should you find between the sample mean and the population mean? - Answer: ANSWER: : a. o = 20 points b. OM = 10 points C. OM= 2 points 75. Each of the following samples was obtained from a population with u = 100 and o= 10. Find the Z-score Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 3. What is measured by the denominator of the z-score test statistic? a. The average distance between M and u that would be expected if Hy was true b. The actual distance between M and u c. The position of the sample mean relative to the critical region d. Whether or not there is a significant difference between M and u - Answer: A 4. Which of the following accurately describes the critical region? a. Outcomes with a very low probability if the null hypothesis is true b. Outcomes with a high probability if the null hypothesis is true c. Outcomes with a very low probability whether or not the null hypothesis is true d. Outcomes with a high probability whether or not the null hypothesis is true - Answer: A 5. A sample of n=25 individuals is selected from a population with u = 80 and a treatment is administered to the sample. What is expected if the treatment has no effect? a. The sample mean should be very different from 80 and should lead you to reject the null hypothesis. Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, b. The sample mean should be very different from 80 and should lead you to fail to reject the null hypothesis. c. The sample mean should be close to 80 and should lead you to reject the null hypothesis. d. The sample mean should be close 80 and should lead you to fail to reject the null hypothesis. - Answer: D 6. A two-tailed hypothesis test is being used to evaluate a treatment effect with a = .05. If the sample data produce a z score of z = 2.24, then what is the correct decision? a. Reject the null hypothesis and conclude that the treatment has no effect. b. Reject the null hypothesis and conclude that the treatment has an effect. c. Fail to reject the null hypothesis and conclude that the treatment has no effect. d. Fail to reject the null hypothesis and conclude that the treatment has an effect. - Answer: B 7. The critical boundaries for a hypothesis test are z=+1.96 and -1.96. If the Z-score for the sample data is z=1.90, Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, then what is the correct statistical decision? a. Fail to reject Hi b. Fail to reject H. c. Reject H d. Reject H - Answer: B 8. A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z=2.37. Assuming that the researcher is using a two-tailed test, what decision should be made? a. The researcher should reject the null hypothesis with a = .05 but not with a=.01. b. The researcher should reject the null hypothesis with either a = .05 or a=.01. c. The researcher should fail to reject Hy with either a=.05 or a=.01. d. The researcher should ignore the results. - Answer: A 9. A researcher conducts a hypothesis test to evaluate the effect of a treatment that is expected to increase scores. The hypothesis test produces a z-score of z= 2.37. If the researcher is using a one-tailed test, what is the correct statistical decision? a. Reject the null Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 14. Even if a treatment has an effect, it is still possible to obtain a sample mean that is very similar to the original population mean. What outcome is likely if this happens? a. Reject Ho and make a Type I error. b. Correctly reject Ho. c. Fail to reject H, and make a Type II error. d. Correctly fail to reject Ho. - Answer: C 15. Which of the following correctly describes the effect of increasing the alpha level (for example, from .01 to .05)? a. Increase the likelihood of rejecting Ho and increase the risk of a Type I error. b. Decrease the likelihood of rejecting Ho and increase the risk of a Type I error. c. Increase the likelihood of rejecting H, and decrease the risk of a Type I error. d. Decrease the likelihood of rejecting Ho and decrease the risk of a Type I error. - Answer: A 16. By selecting a larger alpha level, a researcher is a. attempting to make it more difficult to reject Ho Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, b. less able to detect a treatment effect c. increasing the risk of a Type I error d. decreasing the risk of a Type I error - Answer: C 17. Decreasing the alpha level from a = .05 to a = .01 . a. increases the probability of a Type I error b. increases the size of the critical region c. increases the probability that the sample will fall into the critical region d. decreases the probability of a Type I error - Answer: D 18. Which of the following represents the probability of a Type II error? b. o c. B d. a ANSWER: : C - Answer: C 19. Which of the following is an accurate definition of a Type I error? a. Rejecting a false null hypothesis b. Rejecting a true null hypothesis c. Failing to reject a false null hypothesis d. Failing to reject a true null hypothesis - Answer: B Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 20. Which of the following is an accurate definition of a Type II error? a. Rejecting a false null hypothesis b. Rejecting a true null hypothesis c. Failing to reject a false null hypothesis d. Failing to reject a true null hypothesis - Answer: C 21. What is the consequence of a Type I error? a. Concluding that a treatment has an effect when it really does b. Concluding that a treatment has no effect when it really has no effect c. Concluding that a treatment has no effect when it really does d. Concluding that a treatment has an effect when it really has no effect - Answer: D 22. What is the consequence of a Type II error? a. Concluding that a treatment has an effect when it really does b. Concluding that a treatment has no effect when it really has no effect c. Concluding that a treatment has no effect when it really does d. Concluding that a treatment has an effect when it really has no effect - Answer: C 23. When is there a risk of a Type I error? Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 28. A researcher administers a treatment to a sample of participants selected from a population with u = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? a. A sample mean near 80 for a small sample b. A sample mean near 80 for a large sample c. A sample mean much different than 80 for a small sample d. A sample mean much different than 80 for a large sample - Answer: D 29. A researcher administers a treatment to a sample of participants selected from a population with u = 80. If the researcher obtains a sample mean of M = 88, given the same sample size, which combination of factors is most likely to result in rejecting the null hypothesis? a. o=5 and a = .01 b. o = 5 and a = .05 c. o= 10 and a=.01 d. o= 10 and a=.05 - Answer: B Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 30. A researcher administers a treatment to a sample of participants selected from a population with u = 80. If the researcher obtains a sample mean of M = 88, given the same alpha level, which combination of factors is most likely to result in rejecting the null hypothesis? a. o = 5 and n=25 b. o = 5 and n=50 c. 0= 10 and n=25 d. o= 10 and n= 50 - Answer: B 31. Which combination of factors will increase the chances of rejecting the null hypothesis? a. A large standard error and a large alpha level b. A large standard error and a small alpha level c. A small standard error and a large alpha level d. A small standard error and a small alpha level - Answer: C 32. A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, individuals in a population which is known to have a mean of u = 80. The results will be examined using a one-tailed hypothesis test. Which of the following is the correct statement of the null hypothesis? a. l> 80 b. u > 80 c. u< 80 d. u < 80 - Answer: D 33. A researcher expects a treatment to produce an increase in the population mean. The treatment is evaluated using a one tailed hypothesis test, and the test produces z= +1.85. Based on this result, what is the correct statistical decision? a. The researcher should reject the null hypothesis with a = .05 but not with a = .01. b. The researcher should reject the null hypothesis with either a =.05 or a=.01. c. The researcher should fail to reject Hy with either a=.05 or a=.01. d. The researcher should change a. - Answer: A 34. A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, d. 0.40 - Answer: A 39. Which of the following is an accurate definition for the power of a statistical test? a. The probability of rejecting a true null hypothesis b. The probability of supporting true null hypothesis c. The probability of rejecting a false null hypothesis d. The probability of supporting a false null hypothesis - Answer: C 40. Which of the following will increase the power of a statistical test? a. Change a from .05 to .01 b. Change from a one-tailed test to a two-tailed test c. Change the sample size from n=25 to n= 100 d. None of the other three options will increase the power. - Answer: C 41. The null hypothesis is stated in terms of the population, even though the data come from a sample. a. True b. False - Answer: T 42. In general, the null hypothesis states that the treatment has no effect on the population parameter being studied. Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, a. True b. False - Answer: T 43. The null hypothesis states that the sample mean (after treatment) is equal to the original population mean (before treatment). a. True b. False - Answer: F 44. Most researchers would like the hypothesis test to reject the null hypothesis. a. True b. False - Answer: T 45. The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true. a. True b. False - Answer: T 46. If a hypothesis test leads to rejecting the null hypothesis, it means that the data did not provide enough evidence to conclude that the treatment has an effect. a. True b. False - Answer: F 47. If the sample data are in the critical region with a = .05, then the same sample data would still be in the critical region if a were changed to .01. a. True b. False - Answer: F Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 48. If the sample data are in the critical region with a =.01, then the same sample data would still be in the critical region if a were changed to .05. a. True b. False - Answer: T 49. A Type I error occurs when a treatment actually does have an effect on the scores but the effect was not large enough to reject the null hypothesis. a. True b. False - Answer: F 50. A Type I error occurs when a treatment has no effect but the decision is to reject the null hypothesis. a. True b. False - Answer: T 51. A Type I error occurs when a researcher concludes that a treatment has an effect but, in fact, the treatment has no effect. a. True b. False - Answer: T 52. The alpha level determines the risk of a Type I error. a. True b. False - Answer: T 53. You can reduce the risk of a Type I error by using a larger sample. Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, 63. A measure of effect size is intended to provide a measurement of the absolute magnitude of a treatment effect. a. True b. False - Answer: T 64. The value obtained for Cohen's d is independent of the sample size. a. True b. False - Answer: T 65. A significant treatment effect does not necessarily indicate a large treatment effect. a. True b. False - Answer: T 66. One of the simplest and most direct methods for measuring effect size is Cohen's d. a. True b. False - Answer: T 67. The power of a hypothesis test is the probability that the sample mean will be in the critical region if the treatment has an effect. a. True b. False - Answer: T 68. If the power for a hypothesis test is calculated to be 0.80, then for same test, the probability of a Type II error is 0.20. Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, a. True b. False - Answer: T 69. If all other factors are held constant, increasing the sample size from n= 25 to n= 100 will increase the power of a statistical test. a. True b. False - Answer: T 70. If other factors such as sample size, alpha level, and population standard deviation are held constant, the larger the size of the treatment effect, the greater the power of the hypothesis test. a. True b. False - Answer: T 71. Define the critical region for a hypothesis test, and explain how the critical region is related to the alpha level. - Answer: ANSWER: : The critical region consists of sample outcomes that are very unlikely to occur if the null hypothesis is true. The value of alpha is used to define a precise probability for the term very unlikely. 72. The term error is used in two different ways in hypothesis testing: a Type I error (or Type II) and the standard error. Probability and Sampling, Intro to Hypothesis Testing Chapter 6, 7, 8, a. What can a researcher do to influence the size of the standard error? Does this action have any effect on the probability of a Type I error? b. What can a researcher do to influence the probability of a Type I error? Does this action have any effect on the size of the standard error? - Answer: ANSWER: : a. Increasing the sample size decreases the standard error. Changes in sample size have no effect on the probability of a Type I error. b. The probability of a Type I error is under the direct control of the researcher who selects the alpha level for the test. The choice of an alpha level does not affect the standard error. 73. A researcher would like to determine whether a new tax on cigarettes has had any effect on people's behavior. During the year before the tax was imposed, stores located in rest areas on the state thruway reported selling an average of u = 410 packs per day with o = 60. The distribution of daily sales was approximately normal. For a sample of n= 9 days following the new tax, the researcher found an average of M = 386 packs per day for the same stores. a. Is the sample mean sufficient to conclude that there was a significant change in cigarette purchases after the new tax. Use a two-tailed test with a = .05. b. If the population standard deviation was o=30, is the result sufficient to conclude that there is a significant difference? c. Explain