Review Questions for Final Exam

Review questions for Final Exam

I In the following study one was interested in comparing the reaction time to a stimulus when the subject was under the influence of three different drugs. For this purpose the researcher formed at random four groups of n = 15 subjects. The subjects from Group 1 (control group) received no drug while the subjects from Groups 2, 3 and 4 were treated with drugs A, Band C respectively. The reaction times to the stimulus are tabulated below.

No drug Drug A Drug B Drug C 21.5 12.1 15.1 3 22.4 12.3 15 2.9 23 16.6 15.6 3.7 24.9 10.8 14.9 0.7 20 12.8 22 4.8 27.8 15.7 13 5.7 25.3 19.9 14.5 1.2 22.6 15.2 15.9 5.4 22.3 10.7 11.2 7.6 24.3 15.3 16.2 4.6 23.3 16.9 15.1 0.1 16.3 11.6 17 4.7 20.4 14.1 14.8 4.2 16.3 20.8 15.4 5.1 18.9 14.6 15.9 7.9 x 329.3 219.4 231.6 61.6 x2 7372.13 3340.64 3648.34 324.8

1. Determine the mean reaction time for subjects on Drug B.

2. Determine the median reaction time for subjects who received no drug.

3. Determine the mean reaction time for subjects on Drug A.

4. Determine the median reaction time for subjects on Drug C.

Choices for 1 to 4 a) 4.11 b) 4.60 c) 5.40 d) 12.10 e) 14.63 f) 15.10 g) 15.44 h) 15.90 i) 20.00 j) 22.40

Statistics 244.3 - Review Questions

5. Determine the interquartile range (IQR) of reaction time for subjects who received no drug. 6. Determine the variance (s 2) of reaction time for subjects who received drug B. 7. Determine the standard deviation (s) of reaction time for subjects who received drug A.

Choices for 5 to 7 a) 1.10 b) 1.85 c) 2.27 d) 3.07 e) 3.19 f) 3.33 g) 4.30 h) 5.17 i) 9.40 j) 10.10

8. Identify the stem-leaf diagram for reaction time for subjects who received no drug. 9. Identify the stem-leaf diagram for reaction time for subjects who received drug A. 10. Identify the stem-leaf diagram for reaction time for subjects who received drug B. 11. Identify the stem-leaf diagram for reaction time for subjects who received drug C.

Choices for 8 to 11 a) 0* b) 0* 0.7,0.1,0.7,1.2 1.2 c) 0* 0t 0t 2.9, 3, 3.7 0t 0f 0f 4.2, 4.6, 4.7, 4.8, 5.1, 5.4, 5.7 0f 0s 0s 7.6, 7.9 0s 0 0 0 1* 1* 1* 1t 1t 1t 1f 1f 1f 4.3,5.7 1s 6.3,6.3 1s 1s 1 8.9 1 1 8.9 2* 0.0,0.4, 1.5 2* 2* 0.0,0.4, 1.5 2t 2.3,2.4, 2.6, 3, 3.3 2t 2t 2.3,2.4, 2.6, 3, 3.3 2f 4.3,4.9, 5.3 2f 2f 4.3,4.9, 5.3 2s 7.8 2s 2s 7.8 2 2 2

d) 0* e) 0* f) 0* 0t 0t 0t 0f 0f 0f 0s 0s 0s 0 0 0 1* 0.8,0.7, 1.6, 0.8, 1.7 1.6 1* 1.2 1* 0.8, 1.6 1t 2.1, 2.3, 2.8 1t 3.0 1t 2.1, 2.3, 2.8 1f 4.1, 4.6, 5.2, 5.3, 5.7 1f 4.5, 4.8, 4.9, 5, 5.1, 5.1, 5.4, 5.6, 5.9, 5.9 1f 4.1, 4.6, 5.2, 5.3, 5.7 1s 6.6 , 6.9 1s 6.2, 7 1s 6.6, 6.9 1 9.9 1 1 9.9 2* 0.8 2* 2* 0.8 2t 2t 2.0 2t 2f 2f 2f 2s 2s 2s 2 2 2

12. Identify the box-whisker plot for reaction time for subjects who received no drug. 13. Identify the box-whisker plot for reaction time for subjects who received drug A. 14. Identify the box-whisker plot for reaction time for subjects who received drug B. 15. Identify the box-whisker plot for reaction time for subjects who received drug C. Choices for 12 to 15 50

-10 a b c d e f g h i j Choice 16. Suppose that one is interested in determining if there is a difference in the mean reaction times between the four treatment groups ( no drug, drug A, drug B, drug C). Identify the ANOVA table for carry out this test. Choices: a) Source SS df MS F b) Source SS df MS F Between 1063.90 3 354.63 77.5 Between 2453.94 3 817.98 109.4 Within 256.31 56 4.58 Within 418.71 56 7.48 Total 1320.22 59 Total 2872.65 59 c) Source SS df MS F d) Source SS df MS F Between 175.57 3 58.52 4.0 Between 345.57 3 115.19 3.9 Within 825.65 56 14.74 Within 1634.98 56 29.20 Total 1001.22 59 Total 1980.55 59 e) Source SS df MS F f) Source SS df MS F Between 968.94 3 322.98 19.4 Between 7622.60 3 2540.87 72.2 Within 930.71 56 16.62 Within 1970.71 56 35.19 Total 1899.65 59 Total 9593.32 59 g) Source SS df MS F h) Source SS df MS F Between 2513.94 3 837.98 7.3 Between 22143.94 3 7381.31 84.5 Within 6466.71 56 115.48 Within 4890.71 56 87.33 Total 8980.65 59 Total 27034.65 59

II The following measurements were taken on a sample n = 12 Spruce trees selected at random from a stand. (X = diameter(cm) (at breast height) and Y = height (m)). The data are tabulated below: tree 1 2 3 4 5 6 7 8 9 10 11 12 X (diam) 22.0 16.6 19.4 19.8 18.9 14.1 20.3 5.8 20.0 10.1 15.5 22.9 Y (height) 22.3 18.8 20.2 18.0 20.0 18.5 17.8 8.0 19.2 12.1 16.8 19.8 x = 205.4, y = 211.5, x2 = 3796.38, y2 = 3895.19, xy = 3817.58

17. The value of Sxx is: 18. The value of Syy is: 19. The value of Sxy is: Choices for 17. to 19. a) 122.0 b) 164.7 c) 167.5 d) 177.7 e) 197.4 f) 205.1 g) 241.6 h) 280.6 i) 381.4 j) 398.1

20. The value of Pearsons correlation coefficient r between X (diameter) and Y ( height) is: Choices a) 0.084 b) 0.210 c) 0.244 d) 0.346 e) 0.413 f) 0.469 g) 0.643 h) 0.708 i) 0.911 j) 0.953

21. Determine the value of s, the regression standard deviation. n 2 骣 2 Sxy 琪Hint : (yi- yˆ i ) = S yy - 桫 i=1 Sxx Choices a) 0.866 b) 0.899 c) 1.441 d) 1.692 e) 4.815 f) 5.336 g) 6.673 h) 7.525

22. The slope of the Least Squares line for predicting height (Y) from diameter (X) is: Choices a) -0.60 b) -0.43 c) -0.03 d) 0.70 e) 0.78 f) 1.11 g) 1.61 h) 1.76 i) 1.83 j) 1.93

23. Determine a 95% confidence interval for the slope of the Least Squares line for predicting height (Y) from diameter (X) is: Choices a) 2.944 to 3.576 b) 0.657 to 0.972 c) -0.147 to 1.118 d) -0.477 to 1.037 e) 2.282 to 2.800 f) 2.924 to 3.549 g) 0.478 to 0.929 h) -0.577 to 0.617 i) 2.553 to 3.017 j) 1.377 to 1.609

24. The Y-intercept of the Least Squares line for height (Y) from diameter (X) is:: Choices a) -14.2 b) -12.3 c) -10.4 d) -4.4 e) -2.8 f) -0.6 g) 0.8 h) 2.5 i) 5.58 j) 7.7

25. Determine a 95% confidence interval for the Y-intercept of the Least Squares line for predicting height (Y) from diameter (X) is: Choices a) -2.96 to 6.46 b) 1.58 to 9.59 c) -1.41 to 7.18 d) -4.90 to 3.15 e) -1.43 to 4.65 f) 6.73 to 13.93 g) 0.81 to 5.66 h) 6.37 to 8.05 i) 2.92 to 8.79 j) 2.33 to 11.43

26. Determine the predicted height (Yˆ ) for the 7th tree using the least Squares regression line and its diameter (X): Choices a) 15.5 b) 16.5 c) 17.3 d) 18.9 e) 19.2 f) 19.3 g) 19.4 h) 19.9 i) 21.1 j) 21.7

27. Determine the residual in predicting height (Y) for the 7th tree using the least Squares regression line and its diameter (X): Choices a) -2.06 b) -1.89 c) -1.66 d) -1.51 e) -0.59 f) -0.45 g) 0.31 h) 0.97 i) 1.12 j) 1.24

28. Determine a 95% prediction interval for the height (Y) for the 7th tree using the least Squares regression line and its diameter (X): Choices a) 17.0 to 25.1 b) 14.9 to 22.8 c) 15.9 to 23.9 d) 15.5 to 23.5 e) 11.5 to 19.5 f) 17.6 to 25.8 g) 13.3 to 21.2 h) 15.3 to 23.2 i) 15.7 to 23.6 j) 8.5 to 16.9

29. Determine the proportion of variance in tree-height (Y) that can be explained by tree-diameter (X). Choices a) 0.017 b) 0.182 c) 0.313 d) 0.414 e) 0.488 f) 0.554 g) 0.769 h) 0.829 i) 0.911 j) 0.962

30. Identify the scatter plot for the data

Choices

a) b) 35.0 30.0 30.0 25.0 )

25.0 ) Y Y

20.0 t t h

h 15.0 g

15.0 g i i e e

h 10.0 10.0 h 5.0 5.0 0.0 0.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 diam (X) diam (X) c) d) 50.0 25.0

40.0 20.0 ) ) Y Y

( 15.0 ( 30.0

t t h h g g i i 20.0 10.0 e e h h 10.0 5.0

0.0 0.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 diam (X) diam (X)

e) 35.0 f) 25.0 30.0 20.0 ) ) 25.0 Y Y

( ( 15.0

20.0 t t h h g g 15.0 i i 10.0 e e h h 10.0 5.0 5.0 0.0 0.0 0.0 10.0 20.0 30.0 0.0 10.0 20.0 30.0 diam (X) diam (X)

III The following table lists the smoking habits of a random sample of U of S students.

Gender Male Female Total Non-smoker 135 187 322 g

n Regular Smoker 39 21 60 i k

o Heavy Smoker 5 9 14

m Total 179 217 396 S

31. Estimate the proportion of male U of S students that are nonsmokers. 32. Estimate the proportion of female U of S students that are nonsmokers. 33. Estimate the proportion of smokers that are heavy smokers. Choices a) 0.033 b) 0.189 c) 0.359 d) 0.626 e) 0.696 f) 0.754 g) 0.862 h) 0.912 34. Estimate the proportion of male U of S students that are nonsmokers with a 95% confidence interval. Choices a) 0.691 to 0.817 b) 0.816 to 0.908 c) 0.671 to 0.837 d) 0.801 to 0.922

35. Estimate the proportion of female U of S students that are nonsmokers with a 99% confidence interval. Choices a) 0.691 to 0.817 b) 0.816 to 0.908 c) 0.671 to 0.837 d) 0.801 to 0.922

36. Estimate the difference between males and females in the proportion of nonsmokers with a 95% confidence interval Choices a) 0.030 to 0.186 b) -0.077 to 0.093 c) 0.005 to 0.210 d) 0.015 to 0.386 Suppose one is interested in testing if there is a difference between the proportion of male smokers and female smokers. 37. Determine the appropriate test statistic Choices

pˆ  p pˆ1- p ˆ 2 z  0 z = a) p 1 p  b) 骣1 1 0 0 pˆ(1- p ˆ )琪 + n 桫n1 n 2 pˆ  pˆ pˆ  p z  1 2 z  0 c) pˆ 1 pˆ  pˆ 1 pˆ  d) pˆ 1 pˆ 1 1  2 2   n1 n2 n 38. Determine the value of the test statistic Choices a) 1.75 b) 0.08 c) - 1.06 d) 2. 73 e) -10.2 f) 0.19 g) -3.25 h) 4.2 i) 0. 49 j) 13.8

39. If the significance level of the test is  = 0.05 determine the appropriate critical region Choices a) z > 1.645 b) z < 1.645 c) z < 1.645 or z < 1.645 d) z ≤ -1.645 or z ≥ 1.645 e) z > 1.960 f) z < 1. 960 g) z < -1. 960 or z > 1. 960 h) z ≤ -1. 960 or z ≥ 1. 96 i) z > -1.645 j) z < -1.645

IV. The time X (that it takes a randomly selected patient to metabolize a new drug) has a normal distribution with mean 1.55 hours and standard deviation 0.42 hours.

40. Find the probability that X is at most 2.16. Choices a) 0.092 b) 0.289 c) 0.357 d) 0.551 e) 0.554 f) 0.705 g) 0.786 h) 0.848 i) 0.880 j) 0.927

41. Find the probability that X is at least 1.64. Choices a) 0.012 b) 0.038 c) 0.21 d) 0.377 e) 0.417 f) 0.439 g) 0.522 h) 0.550 i) 0.699 j) 0.733

Suppose that a sample of n = 22 observations of X are taken.

42. Find the probability that the sample mean is less than 1.556 or more than 1.648. Choices a) 0.161 b) 0.164 c) 0.280 d) 0.511 e) 0.551 f) 0.666 g) 0.680 h) 0.739 i) 0.753 j) 0.800

43. Find the probability that the sample mean is between 1.599 and 1.606. Choices a) 0.027 b) 0.152 c) 0.166 d) 0.235 e) 0.427 f) 0.664 g) 0.693 h) 0.782 i) 0.905 j) 0.915

44. Find the probability that the sample mean is at least 1.552. Choices a) 0.097 b) 0.108 c) 0.492 d) 0.544 e) 0.571 f) 0.701 g) 0.729 h) 0.76 i) 0.895 j) 0.905

V. In Canada, 72% of the voters are not in favour of the reinstatement of the death penalty. If three voters were selected at random what is the probability that

45. exactly 2 were not in favour of the death penalty.

46. at most 2 were not in favour of the death penalty.

47. at least 2 were not in favour of the death penalty.

Choices for 45,46,47 a) 0.134 b) 0.280 c) 0.407 d) 0.435 e) 0.627 f) 0.661 g) 0.718 h) 0.720 i) 0.809 j) 0.867

Suppose that a sample of n = 500 cases are observed. Let pˆ denote the proportion of voters in this sample not in favour of the reinstatement of the death penalty.

48. Find the probability that the sample proportion, pˆ , is between 0.696 and 0.742. Choices a) 0.018 b) 0.186 c) 0.391 d) 0.409 e) 0.515 f) 0.557 g) 0.642 h) 0.739 i) 0.854 j) 0.926

49. Find the probability that the sample proportion, pˆ , is at least 0.711. Choices a) 0.275 b) 0.289 c) 0.335 d) 0.38 e) 0.381 f) 0.394 g) 0.516 h) 0.580 i) 0.586 j) 0.674

50. Find the probability that the sample proportion, pˆ , is less than 0.685 or more than 0.726. Choices a) 0.041 b) 0.066 c) 0.237 d) 0.280 e) 0.423 f) 0.580 g) 0.830 h) 0.852 i) 0.880 j) 0.934

Solution Key:

1 g 11 b 21 d 31 f 41 e 2 j 12 h 22 d 32 g 42 f 3 e 13 d 23 g 33 b 43 a 4 b 14 c 24 i 34 a 44 c 5 g 15 i 25 b 35 d 45 d 6 h 16 b 26 h 36 a 46 e 7 d 17 h 27 a 37 b 47 i 8 a 18 c 28 c 38 d 48 h 9 d 19 e 29 h 39 g 49 j 10 e 20 i 30 d 40 j 50 e