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Stats 245.3(02) Term Test 4 Solutions
I.
Monday, March 15, 2010
In the following study a sample of n = 900 males (age 18-25) were asked to
select, in their opinion, the more violent sport between American football and Ice
hockey. The same choice was given to a sample of n = 800 females (age 18-25).
The results are tabulated below:
Males
Females
434
361
466
439
900
800
American
football more
violent
Ice hockey more
violent
Total
1. Estimate the standard deviation of the sample proportion pˆ1 
 pˆ 
1
pˆ1 1  pˆ1 

n1
434
900
434
1  900
  0.0167
900
434
.
900
C
2. Estimate the standard deviation of the sample proportion pˆ 2 
361
.
800
361
361
pˆ 2 1  pˆ 2 
800 1  800 

 0.0176 D
2
n2
800
Choices for 1. to 2.
a) 0.0036
b) 0.0064
c) 0.0167
d) 0.0176
e) 0.0242
f) 0.0395
g) 0.041
h) 0.0457
i) 0.0596
j) 0.0605
3. Determine 95% confidence limits for the proportion of males who consider Ice
hockey more violent.
466
466
pˆ 1  pˆ 
1  900

466
pˆ  z / 2
or 900
 1.960  900
or 0.485 to 0.550 G
n
900
4. Determine 99% confidence limits for the proportion of males who consider
American football more violent.
 pˆ 
434
900
  2.576 
434
900
434
1  900

or 0.439 to 0.525 E
900
5. Determine 95% confidence limits for the proportion of females who consider
American football more violent.
or 0.417 to 0.486 D
6. Determine 99% confidence limits for the proportion of females who consider Ice
hockey more violent.
  2.576 
439
800
439
1  800

or 0.503 to 0.594 A
800
Choices for 3. to 6.
a) 0.503 to 0.594
b) 0.514 to 0.583
c) 0.439 to 0.525
e) 0.475 to 0.561
f) 0.450 to 0.515
g) 0.485 to 0.550
434
800
d) 0.417 to 0.486
h) 0.406 to 0.497
Stats 245.3(02) Term Test 4 Solutions
II.
Monday, March 15, 2010
In the following study, the researcher was interested measuring teacher job
satisfaction and whether it differed significantly amongst the four groups
A. Elementary school teachers who had been teaching less than 5 years. (<5)
B. Elementary school teachers who had been teaching more than 5 years. ( 5)
C. Secondary school teachers who had been teaching less than 5 years. (<5)
D. Secondary school teachers who had been teaching more than 5 years. ( 5)
The researcher decided to choose at random n = 8 teachers from each of the four
groups above. Each teacher was asked to complete a job satisfaction questionnaire
which was scored on a 0-100 scale. The data are tabulated on the next page::
Table: Job Satisfaction Scores
school level
elementary
secondary
# years teaching
<5
<5
5
5
62
75
75
74
67
52
67
66
53
34
54
69
64
39
46
43
66
81
62
69
54
57
58
83
22
44
18
34
20
41
18
47
x 538 402 530 244
x2 36608 21224 35940 8514
7. Compute a 95% confidence interval for the mean job satisfaction score for
elementary school teachers who have taught < 5 years. 60.7 to 73.8 J
8. Compute a 99% confidence interval for the mean job satisfaction score for
secondary school teachers who have taught  5 years. 15.2 to 45.8 D
9. Compute a 95% confidence interval for the mean job satisfaction score for
secondary school teachers who have taught < 5 years. 57.2 to 75.3 B
Choices for 7. and 9.
a) 40.1 to 60.4
f) 57.6 to 76.9
b) 57.2 to 75.3
g) 35.3 to 65.2
c) 52.1 to 66.8
h) 25.7 to 54.9
d) 15.2 to 45.8
i) 52.8 to 79.7
e) 20.2 to 40.8
j) 60.7 to 73.8
10. Compute a 90% confidence interval for the standard deviation of the job
satisfaction score for elementary school teacher who have taught < 5
years. 5.51 to 14.05 G
Choices
a) 8.73 to 22.24
f) 1.32 to 32.21
b) 6.54 to 34.46
g) 5.51 to 14.04
c) 1.22 to 37.1
h) 7.67 to 19.54
d) 2.46 to 26.06
i) 9.6 to 25.54
e) 8.53 to 21.73
j) 7.87 to 39.88
Stats 245.3(02) Term Test 4 Solutions
Monday, March 15, 2010
11. Compute a 90% confidence interval for the difference in the mean job
satisfaction score between elementary school teacher who have taught < 5
years and elementary school teachers who have taught  5 years. (assume
that the standard deviation in job satisfaction score is the same for each
group). 8.04 to 25.96 F
Choices:
a) 0.17 to 12.13
f) 8.04 to 25.96
b) -4.07 to 38.07
g) 7.74 to 11.00
c) 10.15 to 23.85
h) 1.85 to 32.15
d) 3.23 to 23.84
i) 6.08 to 27.92
e) 6.66 to 11.15
j) 8.15 to 18.65
III In each of the following questions consider the three statements A., B. and C,
12. Determine if Statements A., B. and C. are either True (T) or False (F). E
A. A type I error occurs when H0 is accepted when it is in fact false. F
B. P[type I error] = 1 –P[type II error] always. F
C. The significance level of a test is the probability that the test makes a
type I error. T
13. Determine if Statements A., B. and C. are either True (T) or False (F).
A. A 95% confidence interval is wider than a 99% confidence interval. F
B. The critical value from the standard normal distribution, z0.050 = 1.645. T
C. The standard deviation of the sample mean, x , is
x 1  x 
F
n
14. Determine if Statements A., B. and C. are either True (T) or False (F). F
A. When estimating a proportion the (1 – )100% error bound is
pˆ 1  pˆ 
B
F
n
B. When estimating a proportion the (1 – )100% error bound is largest when p
= 0.50. T
C. When estimating a proportion you will double the error bound by doubling
the sample size. F
15. Determine if Statements A., B. and C. are either True (T) or False (F). C
A. The mean of a difference of two random variables is the difference in their
means.  X Y  X  Y  T
B. The standard deviation of a difference of two random variables is the
difference in their standard deviations.  X Y   X  Y  F
C. If n is large then the distribution of the sample mean, x , is normal.T
Choices for 12 to 15.
a) A, B and C are True
c) A and C are True, B is False
e) A and B are False, C is True
g) B and C are False, A is True
b)
d)
f)
h)
A and B are True, C is False
B and C are True, A is False
A and C are False, B is True
A, B and C are False
The End