For Each of the Following Problems, Use the Information Provided And/Or the Normal Curve

Last name: Statistics Problems First name:

For each of the following problems, use the information provided and/or the normal curve below to find a solution. You do not need to show HOW you found a mean (x) or sample standard deviation (s), since those are done using calculator functions, but all other calculations should have work shown.

1. Professor Halen has 184 students in his college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 82 and 90? Express answer to the nearest student.

2. Residents of upstate New York are accustomed to large amounts of snow with snowfalls often exceeding 6 inches in one day. In one city, such snowfalls were recorded for two seasons and are as follows (in inches): 8.6 11. 9.0 7.7 14. 9.2 9.5 5 6.7 6.8 4 7.1 14. 7.0 21. 6.1 6.1 1 8.4 5 8.5 8.0 What are the mean and the population standard deviation for this data, to the nearest hundredth?

3. Neesha's scores in Chemistry this semester were rather inconsistent: 100, 85, 55, 95, 75, 100. For this population, how many scores are within one standard deviation of the mean?

4. From 1984 to 1995, the winning scores for a golf tournament were 276, 279, 279, 277, 278, 278, 280, 282, 285, 272, 279, and 278. Using the standard deviation for this sample, find the percent of these winning scores that fall within one standard deviation of the mean. A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were give a life satisfaction test (known to have high reliability and validity). Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below. Compute the appropriate t-test.

Perceived life satisfaction Mean Std. Dev. Older adults 45 38 52 48 25 39 51 46 55 46 Younger adults 34 22 15 27 37 41 24 19 26 36 1. What would be the null hypothesis in this study?

2. Fill in the information below: a. p: b. Circle one: p < 0.05 p > 0.05 3. Is there a significant difference between the two groups? 4. What conclusion can you draw? Support with the reason you made the decision! 5. 6. In the space below, graph the means and draw error bars to show standard deviation. Label your axes! 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 10 10 10 10 10 10 10 10 10 10 11 11 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 157. 158. A researcher hypothesizes that electrical stimulation of the lateral habenula will result in a decrease in food intake (in this case, chocolate chips) in rats. Rats undergo stereotaxic surgery and an electrode is implanted in the right lateral habenula. Following a ten day recovery period, rats (kept at 80 percent body weight) are tested for the number of chocolate chips consumed during a 10 minute period of time both with and without electrical stimulation. Compute the appropriate t-test for the data provided below. 159. 1 163. 6 Std. 160. 161. Number of chocolate chips consumed per 10 minutes 2. Dev M . 1 1 1 1 1 1 1 1 1 6 6 1 7 6 6 6 7 7 7 17 164. S 5 8 7 4 6 7 9 0 2 3 5. 176. timulation . . 1...... 1 1 14 1 7 3 8 5 7 9

177. N 1 1 1 1 1 1 1 1 1 1 18 189. o 7 7 8 8 8 8 8 8 8 8 8. Stimulatio 8 9 0 1 2 3 4. 5 6 7 n ...... 12 . . . 8 7 4 1 6 7 5 5 8 1. What would be the null hypothesis in this study? 190. 2. Fill in the information below: a. p: b. Circle one: p < 0.05 p > 0.05 3. Is there a significant difference between the two groups? 4. What conclusion can you draw? Support with the reason you made the decision! 5. 6. In the space below, graph the means and draw error bars to show standard deviation. Label your axes! 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 10 10 10 10 10 10 10 10 10 10 11 11 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 157. 158. Twelve cars were equipped with radial tires and driven over a test course. Then the same 12 cars (with the same drivers) were equipped with regular belted tires and driven over the same course. After each run, the cars’ gas economy (in km/l) was measured. Is there evidence that radial tires produce better fuel economy? 159. 1 163. 6 Std. 160. 161. Car 2. D M ev . 1 1 1 1 1 1 1 1 1 1 1 6 6 6 6 6 7 7 7 7 7 7 164. 5 6 7 8 9 0 1 2 3 4 5 176. 177 Radial 178. 5.2 . Tires ...... 4 4. 6 7 6 4 5 6 7 4 6

1 1 1 1 1 1 1 1 1 1 1 192 193. 8 8 8 8 8 8 8 8 8 8 9 . 179. 0 1 2 3 4 5 6 7 8 9 0 191. Belted 4.9 tires ...... 4 4. 6 6 6 4 5 5 6 4 6

1. What would be the null hypothesis in this study? 194. 2. Fill in the information below: a. p: b. Circle one: p < 0.05 p > 0.05 3. Is there a significant difference between the two groups? 4. What conclusion can you draw? Support with the reason you made the decision! 5. 6. In the space below, graph the means and draw error bars to show standard deviation. Label your axes! 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 10 10 10 10 10 10 10 10 10 10 11 11 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 157. 158. Sam Sleepresearcher hypothesizes that people who are allowed to sleep for only four hours will score significantly lower than people who are allowed to sleep for eight hours on a cognitive skills test. He brings sixteen participants into his sleep lab and randomly assigns them to one of two groups. In one group he has participants sleep for eight hours and in the other group he has them sleep for four. The next morning he administers the SCAT (Sam's Cognitive Ability Test) to all participants. (Scores on the SCAT range from 1-9 with high scores representing better performance). 159. 1 163. 6 Std. 160. 161. SCAT score 2. de M v.

1 1 1 1 1 1 1 17 174. 164. 165. 6 6 6 6 7 7 7 3. 8 hrs. 5 sleep 6. 7. 8. 9. 0. 1. 2. 7 5 3 5 3 3 9 1 1 1 1 1 1 1 18 185. 175. 176. 7 7 7 8 8 8 8 4. 4 hrs. 8 sleep 7. 8. 9. 0. 1. 2. 3. 1 4 6 6 4 1 2 1. What would be the null hypothesis in this study? 186. 2. Fill in the information below: a. p: b. Circle one: p < 0.05 p > 0.05 3. Is there a significant difference between the two groups? 4. What conclusion can you draw? Support with the reason you made the decision! 5. 6. In the space below, graph the means and draw error bars to show standard deviation. Label your axes! 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 10 10 10 10 10 10 10 10 10 10 11 11 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 157. 158. 159. A laboratory study was conducted to investigate whether wind speed affects the diameter of the web that orb spiders produce. Therefore, the scientists exposed 20 spiders to low wind speeds (5 km/hr) and another 20 spiders to high wind speeds (15 km/hr) in individual containers. Several days later, the scientists determined the diameter (in mm) of the webs spun by each spider; one spider did not spin a web. Is there a significant difference in the mean diameter of webs spun at high versus low wind speeds? 160. 1 164. 6 Std. 3 D 161. 162. Diameter of webs spun by spiders (mm) . e M v . 1 186. 1 1 1 1 1 1 1 1 1 1 7 1 1 1 1 8 165. 16 178 18 18 Low 6 6 7 7 7 7 7 7 7 7 7 8 8 8 7 9. . 1. 3. wi 6. 7. 0. 1. 2. 3. 4. 5. 6. 9. 0. 4. 5. . 88 . 87 84 nd 68 98 78 91 69 91 83 83 74 5 91 97 73 53

2 209. 2 1 1 1 1 1 1 1 1 1 0 2 2 2 1 188. 19 201 20 20 High 8 9 9 9 9 9 9 9 9 0 0 0 0 20 0 2. . 4. 6. wi 9. 0. 3. 4. 5. 6. 7. 8. 9. 2. 3. 7. 8. . 58 . 62 63 nd 80 60 49 52 47 92 76 79 88 8 72 95 59

1. What would be the null hypothesis in this study? 211. 2. Fill in the information below: a. p: b. Circle one: p < 0.05 p > 0.05 3. Is there a significant difference between the two groups? 4. What conclusion can you draw? Support with the reason you made the decision! 5. 6. In the space below, graph the means and draw error bars to show standard deviation. Label your axes! 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 10 10 10 10 10 10 10 10 10 10 11 11 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 157. 158. An experiment was conducted to determine if growth of a reef-dwelling sponge differed significantly between sponges growing on the top versus the side of the reef. Two tissue samples of equal volume (each 30 cm3) were removed from each of 17 randomly chosen sponges. One tissue sample from each individual sponge was fixed to the top of 17 reefs and the second sample from the same individual sponge was fixed to the side of another 17 reefs (34 reef sites in all). After three months, the volume of each sponge tissue was remeasured and those data are given below. Does orientation on the reef (top vs. side) significantly effect the growth of sponges? 159. 1 163. 6 Std. 2 D 160. 161. Volume of sponge (cm3) . e M v . 1 1 183. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 8 164. 6 6 6 6 7 7 7 7 7 7 7 7 8 8 7 1 2. Top of 5. 6. 7. 8. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 0. . reef 4 3 4 4 4 3 4 4 3 6 6 5 4 4 45 4

1 2 203. 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 9 0 184. 8 8 8 8 9 9 9 9 9 9 9 9 0 0 9 1 2. Side of 5. 6. 7. 8. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 0. . reef 4 4 4 4 4 4 4 3 4 3 4 4 4 3 47 4

1. What would be the null hypothesis in this study? 204. 2. Fill in the information below: a. p: b. Circle one: p < 0.05 p > 0.05 3. Is there a significant difference between the two groups? 4. What conclusion can you draw? Support with the reason you made the decision! 5. 6. In the space below, graph the means and draw error bars to show standard deviation. Label your axes! 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 10 10 10 10 10 10 10 10 10 10 11 11 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 2. 3. 4. 5. 6. 7. 8. 9. 0. 1. 2. 3. 4. 5. 6. 157. 158. 159. A research study was conducted to examine the clinical efficacy of a new antidepressant. Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a low dose of the drug, and a group that received a moderate dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the score, the more depressed the patient. 160. 1 164. 6 162. Beck Depression Std. 161. inventory scores 3. de M v. 1 1 1 1 1 17 172. 6 6 6 6 7 1. 165. 6 7 8 9 0 Placebo . . . . . 3 4 3 2 4

1 1 1 1 17 180. 1 7 7 7 7 9. 7 173. 4 5 7 8 6 Low dose . . . . . 2 1 2 3 8

1 1 1 1 18 188. 1 8 8 8 8 7. 181. 8 2 3 4 5 Moderate 6 . . . . dose . 1 2 1 1 5

1. What would be the null hypothesis in this study? 2. What would be the alternate hypothesis? 3. Fill in the information below: a. p: b. Circle one: p < 0.05 p > 0.0 4. Is there a significant difference between the groups? 5. If there is a significant difference, where specifically are the differences? This is not necessary, but you would conduct a t-test between each combination of pairs to see where it is. 6. What conclusion can you draw? Support with the reason you made the decision! a. A researcher is concerned about the level of knowledge possessed by university students regarding United States history. Students completed a high school senior level standardized U.S. history exam. Major for students was also recorded. Data in terms of percent correct is recorded below for 32 students. b. e. f. c. d. US History Exam score Std

m. n. o. p. q. g. Education h. i. j. k. l.

r. x. y. z. aa. ab. Business/Man s. t. u. v. w. agement ac. ai. aj. ak. al. am. Behaviorhal/S ad. ae. af. ah. ocial science at. au. av. aw. ax. an. Fine Arts ao. ap. aq. ar. as.

1. What would be the null hypothesis in this study? 2. What would be the alternate hypothesis? 3. Fill in the information below: a. p: b. Circle one: p < 0.05 p > 0.0 4. Is there a significant difference between the groups? 5. If there is a significant difference, where specifically are the differences? This is not necessary, but you would conduct a t-test between each combination of pairs to see where it is. 6. What conclusion can you draw? Support with the reason you made the decision! a. Neuroscience researchers examined the impact of environment on rat development. Rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), standard (cage with other rats), enriched (cage with other rats and toys), super enriched (cage with rats and toys changes on a periodic basis). After two months, the rats were tested on a variety of learning measures (including the number of trials to learn a maze to a three perfect trial criteria), and several neurological measure (overall cortical weight, degree of dendritic branching, etc.). b. e. f. c. d. Beck Depression St inventory scores

g. m. n. Imp h. i. j. k. l.

o. u. v. Sta p. q. r. s. t.

w. ac. a Enr x. y. z. ab. d.

ae. ak. al Sup ah. aj. .