University Statistics: Midterm Exam Week 4 Answers and Solutions

This document contains the solutions to a statistics midterm exam, covering a range of topics from chapters 1-6. The solutions include answers to multiple-choice questions, true/false statements, and essay-type problems. Key concepts addressed include relative risk, study designs, binomial distribution, normal distribution calculations, measures of central tendency and dispersion, hypothesis testing, confidence intervals, and probability calculations. The solutions provide detailed explanations and calculations for each problem, including the application of statistical formulas and interpretations of results. The exam also includes questions on sensitivity, specificity, and the analysis of different study types, demonstrating a comprehensive understanding of statistical principles. The document provides step-by-step solutions to ensure clarity and understanding of the concepts.

Midterm Exam Week 4
1

Answers:
SL. ANS SL ANS.
1 C 27 TRUE
2 D 28 0.324
3 B 29 0.623
4 A 30
Mean = 31.67, SD =
5.88, Median = 31.5,
Q1 = 26.75, Q3 =
35.75
5 C 31 0.416
6 D 32 68%
7 B 33 Active- control trial
8 D 34 0.103
9 C 35 Mean = 27.67, SD =
3.28, Median = 28
10 B 36 0.232
11 A 37 0.035
12 TRUE 38 0.209
13 TRUE 39 Cohort study, Case-
control study
14 FALSE 40 CI Men = 1.8%, CI
Women = 1.2%
15 TRUE 41 49.10%
16 FALSE 42 p =0.379
17 FALSE 43 SD = 4.3%
18 TRUE 44
Sensitivity = 0.124
Specificity = 0.028
False negative = 85
19 TRUE 45 RR = 0.907
20 TRUE 46
Mean = 3.168,
Median = 3.165, SD
= 0.236
21 FALSE 47 Sensitivity = 3.8%
22 TRUE 48 p = 0.956
23 TRUE 49 Upper limit = 236.58
24 TRUE 50 Proportion = 0.4625
25 TRUE 51 P(X > 280) = 0.191,
percentile = 32
26 TRUE 52 1.04%
2

Essay Type
Answer:
P = 0.24, n =7
P(X = 1) = C (7, 1)* 0.24^1 * (1 – 0.24) ^6 = 0.324 (Using Binomial)
Answer:
M = 120, S = 16
P(X > 115) = P (Z > (115 – 120)/16) = P(Z > - 0.3125) = 1 – 0.377 = 0.623
Answer:
25 27 31 33 26 28 38 41 24 32 35 40
Mean = (25 + 27 + 31 + 33 + 26 + 28 + 38 + 41 + 24 + 32 + 35+ 40)/12 =31.67
Ascending order:
24 25 26 27 28 31 32 33 35 38 40 41
Median = (12 + 1) / 2 = 6.5th observation = (31 + 32)/ 2 = 31.5
Q1 = (12 + 1) / 4 = 3.25th observation = (26 + 0.25 * (27 – 26)) = 26.25
Q3 = 3*(12 + 1) / 4 = 9.75th observation = (35 + 0.75 (38 – 35)) = 37.25
3

SL X X -31.67 (X - 27.67)^2
1 25 -6.67 44.4889
2 27 -4.67 21.8089
3 31 -0.67 0.4489
4 33 1.33 1.7689
5 26 -5.67 32.1489
6 28 -3.67 13.4689
7 38 6.33 40.0689
8 41 9.33 87.0489
9 24 -7.67 58.8289
10 32 0.33 0.1089
11 35 3.33 11.0889
12 40 8.33 69.3889
Total 380.0 0.0 380.7
SD = √ 380. 7
11 = 5.88
Answer:
P (overweight) = 158 / 380 = 0.416
4

Answer:
Sensitivity = 17/ (17+8) * 100 = 68%
Answer:
The most efficient study design is a Randomized Controlled Trial (RCT). In cases of
pharmaceutical trials due to a given drug already on the market will make it an active-
control trial.
Answer:
P = 0.3, n =10
P(X = 5) = C (10, 5)* 0.3^5 * (1 – 0.3) ^5 = 0.103 (Using Binomial)
5

Answer:
29 26 24 32 30 22 27 28 31
Mean = (29 + 26 + 24 + 32 + 30 + 22 + 27 + 28 + 31)/9 = 27.67
Ascending order:
22 24 26 27 28 29 30 31 32
Median = 5th observation = 28
SL X X -27.67 (X - 27.67)^2
1 29 1.33 1.7689
2 26 -1.67 2.7889
3 24 -3.67 13.4689
4 32 4.33 18.7489
5 30 2.33 5.4289
6 22 -5.67 32.1489
7 27 -0.67 0.4489
8 28 0.33 0.1089
9 31 3.33 11.0889
Total 249.0 0.0 86.0
SD = √ 86
8 =3. 278 = 3.28 (APPROX 2 DECIMALS)
6

Answer:
People in U.S urban neighbourhood = 215
People overweight and living in U.S urban neighbourhood = 50
Required probability = 50 / 215 = 0.232
Answer:
P = 0.2, n =15
P(X = 0) = C (15, 0) *0.2^0 * (1 – 0.2) ^15 = 0.035 (Using Binomial)
Answer:
M = 24.5, S = 6.2
P(X > 25) = P (Z > (25 – 24.5)/6.2) = P (Z > 0.81) = 1 – 0.791 = 0.209
Answer:
Cohort study: that meets a set of criteria and is used to make an association between a certain
risk factor and developing a disease.
Case-Control study: Useful for rare condition.
7

Answer:
Cumulative incidence of AF in men = 120 / (120 + 6453) = 0.018 = 1.8%
Cumulative incidence of AF in men and in women = 86 / (86 + 7074) = 0.012 = 1.2%
Answer:
Total cell phone users = 65 + 78 = 143
Sample size = 55 + 31 + 65 + 78 + 35 + 27 = 291
Proportion of cell phone users = 143 / 291 = 0.491 = 49.1%
Answer:
M = 89 ng/mL, S = 23 ng/mL, n = 50
8

P(X-bar > 90) = P (Z > (90 –89)/ (23/ sqrt (50)) = P (Z > 0.307) = 1 – 0.621 = 0.379
Answer:
Participant
ID Before Intervention After Intervention Diff Diff - 0.03 (Diff-0.03)^2
1 0.75 0.80 0.05 0.02 0.0004
2 0.82 0.84 0.02 -0.01 0.0001
3 0.66 0.70 0.04 0.01 0.0001
4 0.74 0.70 -0.04 -0.07 0.0049
5 0.88 0.90 0.02 -0.01 0.0001
6 0.66 0.75 0.09 0.06 0.0036
7 0.51 0.60 0.09 0.06 0.0036
8 0.93 0.90 -0.03 -0.06 0.0036
9 0.88 0.90 0.02 -0.01 0.0001
10 0.91 0.95 0.04 0.01 0.0001
Total 7.74 8.04 0.30 0.00 0.0166
SD of the difference in adherence = √ ( 0 .166 / 9 ) =0 . 043=4 . 3 %
9

Answer:
Sensitivity = 12 / (12 + 85) = 0.124 = 12.4%
Specificity = 6 / (6 + 204) = 0.028 = 2.8%
False negative = 85
Answer:
New Drug Placebo
Progress 28 38
Not
Progress 172 162
RR =
28
28+32
172
172+162
= 0 . 467
0 . 515 =0 . 907
10

Answer:
3.282.97 3.05 3.61 3.39 2.95 3.00 3.10
SL X X - 3.168 (X - 3.168)^2
1 3.28 0.112 0.0125
2 2.97 -0.198 0.0392
3 3.05 -0.118 0.0139
4 3.61 0.442 0.1954
5 3.39 0.222 0.0493
6 2.95 -0.218 0.0475
7 3 -0.168 0.0282
8 3.1 -0.068 0.0046
Total 25.35 0.006 0.390692
Mean = 25.35 / 8 = 3.168
SD = √ 0 . 391
7 =0 .236
Ascending Order:
2.95 2.97 3 3.05 3.28 3.39 3.61
Median = (8 + 1)/ 2 = 4.5th observation = (3.05 + 3.28)/ 2 = 3.165
Answer:
11

Sensitivity = 51 / (51 + 1274) = 0.038 = 3.8%
Answer:
P (Adequate dental care / Child from US) =
P ( Adequate dental care∩Child from US )
P ( Child from US ) =
4563
12222
4772
12222
= 0 .373
0 .390 =0. 956
Answer:
Let Upper limit = A
P (X < A) = 0.95
=>P (Z < (A – 205)/ 19.2) = 0.95 = P (Z < 1.645)
=> Upper limit A = 205 + 19.2 * 1.645 = 236.584
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