Download Statistics 246

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.
x 
x2 
No drug
Drug A
Drug B
Drug C
21.5
22.4
23
24.9
20
27.8
25.3
22.6
22.3
24.3
23.3
16.3
20.4
16.3
18.9
12.1
12.3
16.6
10.8
12.8
15.7
19.9
15.2
10.7
15.3
16.9
11.6
14.1
20.8
14.6
15.1
15
15.6
14.9
22
13
14.5
15.9
11.2
16.2
15.1
17
14.8
15.4
15.9
3
2.9
3.7
0.7
4.8
5.7
1.2
5.4
7.6
4.6
0.1
4.7
4.2
5.1
7.9
329.3
219.4
231.6
61.6
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
f) 15.10
g) 15.44
c) 5.40
h) 15.90
Page 1
d) 12.10
i) 20.00
e) 14.63
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
f) 3.33
g) 4.30
8.
9.
10.
11.
c) 2.27
h) 5.17
d) 3.07
i) 9.40
e) 3.19
j) 10.10
Identify the stem-leaf diagram for reaction time for subjects who received no drug.
Identify the stem-leaf diagram for reaction time for subjects who received drug A.
Identify the stem-leaf diagram for reaction time for subjects who received drug B.
Identify the stem-leaf diagram for reaction time for subjects who received drug C.
Choices for 8 to 11
a)
d)
0*
0t
0f
0s
0
1*
1t
1f
1s
1
2*
2t
2f
2s
2
b)
6.3,6.3
8.9
0.0,0.4, 1.5
2.3,2.4, 2.6, 3, 3.3
4.3,4.9, 5.3
7.8
0*
0t
0f
0s
0
0.7,1.6,
0.8,1.71.6
1* 0.8,
1t 2.1, 2.3, 2.8
1f 4.1, 4.6, 5.2, 5.3, 5.7
1s 6.6 , 6.9
1 9.9
2* 0.8
2t
2f
2s
2
e)
0*
0t
0f
0s
0
1*
1t
1f
1s
1
2*
2t
2f
2s
2
0*
0t
0f
0s
0
1*
1t
1f
1s
1
2*
2t
2f
2s
2
0.7,
1.2
0.1,0.7,1.2
2.9, 3, 3.7
4.2, 4.6, 4.7, 4.8, 5.1, 5.4, 5.7
7.6, 7.9
c)
f)
1.2
3.0
4.5, 4.8, 4.9, 5, 5.1, 5.1, 5.4, 5.6, 5.9, 5.9
6.2, 7
2.0
Page 2
0*
0t
0f
0s
0
1*
1t
1f
1s
1
2*
2t
2f
2s
2
0*
0t
0f
0s
0
1*
1t
1f
1s
1
2*
2t
2f
2s
2
4.3,5.7
8.9
0.0,0.4, 1.5
2.3,2.4, 2.6, 3, 3.3
4.3,4.9, 5.3
7.8
0.8, 1.6
2.1, 2.3, 2.8
4.1, 4.6, 5.2, 5.3, 5.7
6.6, 6.9
9.9
0.8
Statistics 244.3 - Review Questions
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
40
30
Y
20
10
0
-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)
c)
e)
g)
Source
SS
df
MS
F
Between
Within
1063.90
256.31
3
56
354.63
4.58
77.5
Total
1320.22
59
Source
SS
df
MS
F
Between
Within
175.57
825.65
3
56
58.52
14.74
4.0
Total
1001.22
59
Source
SS
df
MS
F
Between
Within
968.94
930.71
3
56
322.98
16.62
19.4
Total
1899.65
59
Source
SS
df
MS
F
Between
Within
2513.94
6466.71
3
56
837.98
115.48
7.3
Total
8980.65
59
b)
Source
SS
df
MS
F
Between
Within
2453.94
418.71
3
56
817.98
7.48
109.4
Total
2872.65
59
Source
SS
df
MS
F
Between
Within
345.57
1634.98
3
56
115.19
29.20
3.9
Total
1980.55
59
Source
SS
df
MS
F
Between
Within
7622.60
1970.71
3
56
2540.87
35.19
72.2
Total
9593.32
59
d)
f)
h)
Source
SS
df
MS
F
Between
Within
22143.94
4890.71
3
56
7381.31
87.33
84.5
Total
27034.65
59
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Statistics 244.3 - Review Questions
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, x = 3796.38, y = 3895.19, xy = 3817.58
2
2

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
f) 205.1
g) 241.6
20.
c) 167.5
h) 280.6
d) 177.7
i) 381.4
e) 197.4
j) 398.1
The value of Pearsons correlation coefficient r between X (diameter) and
Y ( height) is:
Choices
a) 0.084
f) 0.469
b) 0.210
g) 0.643
c) 0.244
h) 0.708
d) 0.346
i) 0.911
e) 0.413
j) 0.953
21. Determine the value of s, the regression standard deviation.
n

S xy2 
2
 Hint :  ( yi  yˆ i )  S yy 

S xx 
i 1

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
f) 1.11
23.
b) -0.43
g) 1.61
c) -0.03
h) 1.76
d) 0.70
i) 1.83
e) 0.78
j) 1.93
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
f) 2.924 to 3.549
24.
Choices
a) -14.2
f) -0.6
b) 0.657 to 0.972
g) 0.478 to 0.929
c) -0.147 to 1.118
h) -0.577 to 0.617
d) -0.477 to 1.037
i) 2.553 to 3.017
e) 2.282 to 2.800
j) 1.377 to 1.609
The Y-intercept of the Least Squares line for height (Y) from diameter (X)
is::
b) -12.3
g) 0.8
c) -10.4
h) 2.5
Page 4
d) -4.4
i) 5.58
e) -2.8
j) 7.7
Statistics 244.3 - Review Questions
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
f) 6.73 to 13.93
26.
b) 1.58 to 9.59
g) 0.81 to 5.66
c) -1.41 to 7.18
h) 6.37 to 8.05
d) -4.90 to 3.15
i) 2.92 to 8.79
e) -1.43 to 4.65
j) 2.33 to 11.43
 
Determine the predicted height Yˆ for the 7th tree using the least Squares
regression line and its diameter (X):
Choices
a) 15.5
f) 19.3
27.
b) 16.5
g) 19.4
d) 18.9
i) 21.1
e) 19.2
j) 21.7
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
f) -0.45
28.
c) 17.3
h) 19.9
b) -1.89
g) 0.31
c) -1.66
h) 0.97
d) -1.51
i) 1.12
e) -0.59
j) 1.24
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
f) 17.6 to 25.8
29.
Choices
a) 0.017
f) 0.554
b) 14.9 to 22.8
g) 13.3 to 21.2
c) 15.9 to 23.9
h) 15.3 to 23.2
d) 15.5 to 23.5
i) 15.7 to 23.6
e) 11.5 to 19.5
j) 8.5 to 16.9
Determine the proportion of variance in tree-height (Y) that can be explained
by tree-diameter (X).
b) 0.182
g) 0.769
c) 0.313
h) 0.829
Page 5
d) 0.414
i) 0.911
e) 0.488
j) 0.962
Statistics 244.3 - Review Questions
30.
Identify the scatter plot for the data
Choices
a)
b)
35.0
30.0
25.0
25.0
height ( Y)
height ( Y)
30.0
20.0
15.0
10.0
20.0
15.0
10.0
5.0
5.0
0.0
0.0
0.0
10.0
20.0
30.0
0.0
diam (X)
25.0
40.0
20.0
height ( Y)
height ( Y)
d)
50.0
30.0
20.0
10.0
5.0
0.0
0.0
20.0
0.0
30.0
f)
35.0
20.0
30.0
25.0
30.0
20.0
25.0
height ( Y)
height ( Y)
10.0
diam (X)
diam (X)
e)
30.0
15.0
10.0
10.0
20.0
diam (X)
c)
0.0
10.0
20.0
15.0
10.0
15.0
10.0
5.0
5.0
0.0
0.0
0.0
10.0
20.0
30.0
0.0
10.0
20.0
diam (X)
diam (X)
Page 6
30.0
Statistics 244.3 - Review Questions
Smoking
III The following table lists the smoking habits of a random sample of U of S students.
Gender
Male
Female
Non-smoker
135
187
Regular Smoker 39
21
Heavy Smoker
5
9
Total
179
217
Total
322
60
14
396
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 0
pˆ1  pˆ 2
a) z 
b) z 
p 0 1  p 0 
1 1
pˆ 1  pˆ    
n
 n1 n2 
pˆ 1  pˆ 2
d)
pˆ 1 1  pˆ 1  pˆ 2 1  pˆ 2 

n1
n2
38. Determine the value of the test statistic
Choices
c)
a) 1.75
f) 0.19
z
b) 0.08
g) -3.25
c) - 1.06
h) 4.2
z
d)
i)
Page 7
pˆ  p0
pˆ 1  pˆ 
n
2. 73
0. 49
e)
j)
-10.2
13.8
Statistics 244.3 - Review Questions
39. If the significance level of the test is  = 0.05 determine the appropriate critical
region
Choices
a) z > 1.645
e) z > 1.960
i) z > -1.645
b) z < 1.645
f) z < 1. 960
j) z < -1.645
c) z < 1.645 or z < 1.645
g) z < -1. 960 or z > 1. 960
d) z ≤ -1.645 or z ≥ 1.645
h) z ≤ -1. 960 or z ≥ 1. 96
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
Page 8
Statistics 244.3 - Review Questions
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
f) 0.661
g) 0.718
c) 0.407
h) 0.720
d) 0.435
i) 0.809
e) 0.627
j) 0.867
Suppose that a sample of n = 500 cases are observed. Let p̂ 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, p̂ , 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, p̂ , 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, p̂ , 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
Page 9
Statistics 244.3 - Review Questions
Solution Key:
1
2
3
4
5
6
7
8
9
10
g
j
e
b
g
h
d
a
d
e
11
12
13
14
15
16
17
18
19
20
b
h
d
c
i
b
h
c
e
i
21
22
23
24
25
26
27
28
29
30
d
d
g
i
b
h
a
c
h
d
31
32
33
34
35
36
37
38
39
40
Page 10
f
g
b
a
d
a
b
d
g
j
41
42
43
44
45
46
47
48
49
50
e
f
a
c
d
e
i
h
j
e