Use the chi–square table to find the required 2–value(s).
60)
For a 2–curve with 25 degrees of freedom, find the 2–value having area 0.005 to its right.
60)
A)
10.520
B)
45.559
C)
37.653
D)
46.928
The sample standard deviations and sample sizes are given for independent simple random samples from two
populations. Use the two–standard–deviations F–test to conduct the required hypothesis test.
61)
s1=26.9, n1= 61, s2=26.3, n2= 31; right–tailed test, = 0.01
61)
A)
Test statistic: F =27.51. Critical value = 2.03. Reject H0.
B)
Test statistic: F =1.05. Critical value = 2.21. Do not reject H0.
C)
Test statistic: F =1.05. Critical value = 2.03. Reject H0.
D)
Test statistic: F =1.02. Critical value = 2.21. Do not reject H0.
A sample standard deviation and sample size are given. Use the one–standard–deviation 2–test to conduct the required
hypothesis test.
62)
s =4.6, n = 17
H0: =3.5, Ha: 3.5, = 0.10
62)
A)
Test statistic: X2=27.637. Critical values = 7.962, 26.296. Reject H0.
B)
Test statistic: X2=27.637. Critical values = 9.312, 23.542. Reject H0.
C)
Test statistic: X2= 9.870. Critical values = 9.312, 23.542. Do not reject H0.
D)
Test statistic: X2= 9.870. Critical values = 7.962, 26.296. Do not reject H0.
Use the chi–square table to find the required 2–value(s).
63)
For a 2–curve with df = 5, determine 2
0.995 .
63)
A)
0.207
B)
0.412
C)
1.145
D)
16.750
The sample standard deviations and sample sizes are given for independent simple random samples from two
populations. Use the two–standard–deviations F–test to conduct the required hypothesis test.
64)
s1=20.4 , n1= 16, s2=22.3 , n2= 13; two–tailed test, = 0.05
64)
A)
Test statistic: F =0.84. Critical values = 0.338, 3.18. Reject H0.
B)
Test statistic: F =0.84. Critical values = 0.338, 3.18. Do not reject H0.
C)
Test statistic: F =0.84. Critical values = 0.314, 3.18. Do not reject H0.
D)
Test statistic: F =0.84. Critical values = 0.403, 2.62. Reject H0.
Provide an appropriate response.
65)
True or False? The 2–test for one population standard deviation is robust to moderate violations
of the normality assumption.
65)
A)
True
B)
False
Use the two–standard–deviations F–interval procedure to find the required confidence interval. Assume that independent
samples have been randomly selected from the two populations and that the variable under consideration is normally
distributed on both populations.
66)
A researcher obtained independent random samples of men from two different towns. She
recorded the weights of the men. The results are summarized below:
Town A Town B
n1= 61 n2= 31
x1= 165.1 lb x2= 159.5 lb
s =28.5 lb s =26.8 lb
Construct a 99% confidence interval for the ratio, 1/2, where 1 is the population standard
deviation of the weights of men from town A and 2 is the population standard deviation of the
weights of men from town B.
66)
A)
0.684 to 1.574
B)
0.715 to 1.515
C)
0.684 to 1.654
D)
0.439 to 2.329
Provide an appropriate response.
67)
True or false? F0.01 for an F–curve with df = (11, 13) is equal to 1/F0.01 for an F–curve with
df = (13, 11).
67)
A)
True
B)
False
A sample standard deviation and sample size are given. Use the one–standard–deviation 2–interval procedure to obtain
the specified confidence interval.
68)
s =7, n =22 , 99% confidence interval
68)
A)
5.141 to 10.754
B)
4.985 to 11.317
C)
0.775 to 3.993
D)
1.884 to 4.278
Use the two–standard–deviations F–interval procedure to find the required confidence interval. Assume that independent
samples have been randomly selected from the two populations and that the variable under consideration is normally
distributed on both populations.
69)
The manager of a juice bottling factory is considering installing a new juice bottling machine which
she hopes will reduce the amount of variation in the volumes of juice dispensed into 8–fluid–ounce
bottles. Random samples of 10 bottles filled by the old machine and 9 bottles filled by the new
machine yielded the following volumes of juice (in fluid ounces).
Old machine: 8.1, 8.0, 8.0, 7.8, 8.0, 8.1, 8.0, 8.1, 8.1, 8.0
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1
Construct a 90% confidence interval for the ratio, 1/2, where 1 is the population standard
deviation of the volumes of juice dispensed by the old machine and 2 is the population standard
deviation of the volumes of juice dispensed by the new machine. (Note: s1=0.0919, s2= 0.0782)
69)
A)
0.64 to 2.11
B)
0.74 to 2.30
C)
0.55 to 2.02
D)
0.92 to 2.57
Use the chi–square table to find the required 2–value(s).
70)
For a 2–curve with df = 21, determine 2
0.05 .
70)
A)
8.034
B)
11.591
C)
32.671
D)
41.401
Provide an appropriate response.
71)
True or false? A 2–curve with 10 degrees of freedom is more skewed than a 2–curve with 12
degrees of freedom.
71)
A)
True
B)
False
Use the F–table and the reciprocal property of F–curves, if necessary, to find the required F–value(s).
72)
An F–curve has df = (15, 10). Find the F–value having area 0.05 to its left.
72)
A)
2.54
B)
0.394
C)
0.351
D)
2.85
Provide an appropriate response.
73)
For a given 2–curve, rank the following 2–values in ascending order: 2
0.01 , 2
0.9 , 2
0.1 ,
2
0.99 .
73)
A)
2
0.1 , 2
0.01 , 2
0.99 , 2
0.9
B)
2
0.9 , 2
0.99 , 2
0.01 , 2
0.1
C)
2
0.99 , 2
0.9 , 2
0.1 , 2
0.01
D)
2
0.01 , 2
0.1 , 2
0.9 , 2
0.99
Use the one–standard–deviation chi–square interval procedure to obtain the specified confidence interval for the
population standard deviation . Assume that the population has a normal distribution.
74)
The mean systolic blood pressure for a random sample of 28 women aged 18–24 is 115.8 mm Hg
and the standard deviation is 13.5 mm Hg. Construct a 90% confidence interval for the standard
deviation , of the systolic blood pressures of all women aged 18–24.
74)
A)
11.1 to 17.5 mm Hg
B)
10.5 to 18.9 mm Hg
C)
11.6 to 16.5 mm Hg
D)
10.9 to 17.0 mm Hg
Use the chi–square table to find the required 2–value(s).
75)
For a 2–curve with 23 degrees of freedom, find the 2–value having area 0.995 to its right.
75)
A)
9.260
B)
13.091
C)
9.886
D)
44.181
Provide an appropriate response.
76)
True or false? The F–test for two population standard deviations is robust to moderate violations of
the normality assumption.
76)
A)
True
B)
False
77)
True or false? A 2–curve starts at zero and extends indefinitely to the right.
77)
A)
True
B)
False
B)
Use the one–standard–deviation chi–square interval procedure to obtain the specified confidence interval for the
population standard deviation . Assume that the population has a normal distribution.
78)
A sociologist develops a test to assess attitudes about public transportation, and 27 randomly
selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct a 95% confidence interval for the standard deviation, , of the scores of all subjects.
78)
A)
16.6 to 28.6
B)
16.9 to 29.3
C)
17.5 to 27.8
D)
17.2 to 27.2
B)
The sample standard deviations and sample sizes are given for independent simple random samples from two
populations. Use the two–standard–deviations F–test to conduct the required hypothesis test.
79)
s1=19.9 , n1= 16, s2=22.3 , n2= 13; left–tailed test, = 0.10
79)
A)
Test statistic: F =0.8. Critical value = 0.476. Do not reject H0.
B)
Test statistic: F =0.8. Critical value = 0.495. Reject H0.
C)
Test statistic: F =0.8. Critical value = 0.476. Reject H0.
D)
Test statistic: F =0.8. Critical value = 0.495. Do not reject H0.
B)
B)
A sample standard deviation and sample size are given. Use the one–standard–deviation 2–test to conduct the required
hypothesis test.
80)
s =4.7, n = 29
H0: =5.2, Ha: <5.2, = 0.025
80)
A)
Test statistic: X2=22.874. Critical value = 15.308. Reject H0.
B)
Test statistic: X2= 21.182. Critical value = 44.461. Do not reject H0.
C)
Test statistic: X2=22.874. Critical value = 44.461. Reject H0.
D)
Test statistic: X2=22.874. Critical value = 15.308. Do not reject H0.
Use the F–table and the reciprocal property of F–curves, if necessary, to find the required F–value(s).
81)
An F–curve has df = (20, 9). Find F0.05 .
81)
A)
2.94
B)
2.39
C)
0.418
D)
5.83
Use the two–standard–deviations F–interval procedure to find the required confidence interval. Assume that independent
samples have been randomly selected from the two populations and that the variable under consideration is normally
distributed on both populations.
82)
When 16 randomly selected customers enter a single main waiting line at a bank, their waiting
times have a standard deviation of 2.45 minutes. When 25 randomly selected customers enter any
one of several waiting lines, their waiting times have a standard deviation of 5.12 minutes.
Construct a 98% confidence interval for the ratio, 1/2, where 1 is the population standard
deviation of the waiting times when a single line is used and 2 is the population standard
deviation of the waiting times when several lines are used.
82)
A)
1.406 to 2.977
B)
1.229 to 3.791
C)
1.229 to 3.251
D)
0.864 to 4.577
Use the F–table and the reciprocal property of F–curves, if necessary, to find the required F–value(s).
83)
An F–curve has df = (3, 5). Find the F–value having area 0.01 to its right.
83)
A)
28.24
B)
0.035
C)
3.62
D)
12.06
84)
An F–curve has df = (30, 3). Find the F–value having area 0.90 to its left.
84)
A)
0.193
B)
5.17
C)
2.28
D)
0.439
A sample standard deviation and sample size are given. Use the one–standard–deviation 2–interval procedure to obtain
the specified confidence interval.
85)
s =7, n =13 , 95% confidence interval
85)
A)
5.288 to 10.607
B)
5.02 to 4.367
C)
1.039 to 5.506
D)
5.02 to 11.555
Use the chi–square table to find the required 2–value(s).
86)
For a 2–curve with 20 degrees of freedom, find the 2–value having area 0.99 to its left.
86)
A)
7.633
B)
28.412
C)
8.260
D)
37.566
The sample standard deviations and sample sizes are given for independent simple random samples from two
populations. Use the two–standard–deviations F–test to conduct the required hypothesis test.
87)
s1=5.26, n1= 25, s2=2.5, n2= 17; right–tailed test, = 0.01
87)
A)
Test statistic: F =2.1. Critical value = 3.18. Do not reject H0.
B)
Test statistic: F =4.43. Critical value: F = 3.18. Do not reject H0.
C)
Test statistic: F =2.1. Critical value = 1.87. Reject H0.
D)
Test statistic: F =4.43. Critical value: F = 3.18. Reject H0.
A sample standard deviation and sample size are given. Use the one–standard–deviation 2–test to conduct the required
hypothesis test.
88)
s =10, n =12
H0: =9, Ha: 9, = 0.05
88)
A)
Test statistic: X2=13.58, Critical values =4.575, 19.675. Do not reject H0.
B)
Test statistic: X2=8.91, Critical values =4.575, 19.675. Reject H0.
C)
Test statistic: X2=13.58, Critical values =3.816, 21.92. Do not reject H0.
D)
Test statistic: X2=8.91, Critical values =3.816, 21.92. Do not reject H0.
Provide an appropriate response.
89)
True or false? The two 2–values that divide the area under a 2–curve into a middle 0.9 area and
two outside 0.05 areas are 2
0.9 and 2
0.1 .
89)
A)
True
B)
False
Use the F–table and the reciprocal property of F–curves, if necessary, to find the required F–value(s).
90)
An F–curve has df = (9, 7). Find F0.01 .
90)
A)
2.51
B)
2.72
C)
5.61
D)
6.72
Use the two–standard–deviations F–interval procedure to find the required confidence interval. Assume that independent
samples have been randomly selected from the two populations and that the variable under consideration is normally
distributed on both populations.
91)
A researcher is interested in comparing the amount of variation in women’s scores on a certain test
and the amount of variation in men’s scores on the same test. Independent random samples of 11
men and 13 women yielded the following scores.
Men: 72, 60, 52, 87, 66, 74, 95, 50, 81, 70, 72
Women: 70, 78, 62, 96, 75, 68, 41, 74, 80, 47, 73, 94, 65
Construct a 95% confidence interval for the ratio, 1/2, where 1 is the population standard
deviation of the scores for men and 2 is the population standard deviation of the scores for
women.
(Note: s1= 13.754 and s2= 15.588)
91)
A)
0.48 to 1.62
B)
0.62 to 2.16
C)
0.26 to 3.20
D)
0.48 to 1.68
Use the one–standard–deviation chi–square interval procedure to obtain the specified confidence interval for the
population standard deviation . Assume that the population has a normal distribution.
92)
The weights of 22 randomly selected eggs have a mean, x, of 1.78 oz and a standard deviation, s, of
0.42 oz. Determine a 95% confidence interval for the standard deviation, , of the weights of all
such eggs.
92)
A)
0.32 to 0.58 oz
B)
0.34 to 0.57 oz
C)
0.32 to 0.60 oz
D)
0.33 to 0.55 oz
A sample standard deviation and sample size are given. Use the one–standard–deviation 2–test to conduct the required
hypothesis test.
93)
s =978, n = 22
H0: =650, Ha: >650, = 0.01
93)
A)
Test statistic: X2= 37.115. Critical value = 38.932. Do not reject H0.
B)
Test statistic: X2= 37.115. Critical value = 38.932. Reject H0.
C)
Test statistic: X2=47.541. Critical value = 38.932. Do not reject H0.
D)
Test statistic: X2=47.541. Critical value = 38.932. Reject H0.
Use the F–table and the reciprocal property of F–curves, if necessary, to find the required F–value(s).
94)
An F–curve has df = (12, 15). Find F0.005 .
94)
A)
2.48
B)
4.72
C)
2.62
D)
4.25
Use the one–standard–deviation chi–square interval procedure to obtain the specified confidence interval for the
population standard deviation . Assume that the population has a normal distribution.
95)
The amounts (in ounces) of juice in eight randomly selected juice bottles are:
15.4 15.1 15.9 15.0
15.1 15.5 15.6 15.2
Find a 98% confidence interval for the standard deviation, , of the amounts of juice in all such
bottles.
95)
A)
0.21 to 0.81 oz
B)
0.18 to 0.63 oz
C)
0.19 to 0.73 oz
D)
0.19 to 0.63 oz
96)
The daily intakes of milk (in ounces) for ten five–year old children selected at random from one
school were:
20.0 12.1 16.5 31.6 31.4
11.8 22.3 11.3 21.5 18.6
Find a 99% confidence interval for the standard deviation, , of the daily milk intakes of all
five–year olds at this school.
96)
A)
4.56 to 16.82 oz
B)
0.97 to 3.55 oz
C)
4.41 to 15.11 oz
D)
4.56 to 15.11 oz
Provide an appropriate response.
97)
True or false? F0.95 for an F–curve with df = (25, 26) is equal to F0.05 for an F–curve with
df = (26, 25).
97)
A)
True
B)
False
The sample standard deviations and sample sizes are given for independent simple random samples from two
populations. Use the two–standard–deviations F–test to conduct the required hypothesis test.
98)
s1=5.26, n1= 31, s2=4.75 , n2= 25; two–tailed test, = 0.10
98)
A)
Test statistic: F =1.23. Critical values = 0.529, 1.94. Do not reject H0.
B)
Test statistic: F =1.23. Critical values = 0.515, 1.94. Do not reject H0.
C)
Test statistic: F =1.11. Critical values = 0.515, 1.94. Reject H0.
D)
Test statistic: F =1.11. Critical values = 0.529, 1.94. Do not reject H0.
A sample standard deviation and sample size are given. Use the one–standard–deviation 2–test to conduct the required
hypothesis test.
99)
s =13, n =10
H0: =8, Ha: >8, = 0.05
99)
A)
Test statistic: X2=3.408, Critical value =16.919. Do not reject H0.
B)
Test statistic: X2=23.766, Critical value =16.919. Reject H0.
C)
Test statistic: X2=23.766, Critical value =19.023. Reject H0.
D)
Test statistic: X2=3.408, Critical value =19.023. Do not reject H0.
Use the F–table and the reciprocal property of F–curves, if necessary, to find the required F–value(s).
100)
An F–curve has df = (24, 3). Find the F–value having area 0.005 to its right.
100)
A)
5.52
B)
0.181
C)
8.64
D)
42.62
Use the one–standard–deviation chi–square interval procedure to obtain the specified confidence interval for the
population standard deviation . Assume that the population has a normal distribution.
101)
The weights of 14 men selected at random from one town have a mean, x, of 161.8 lb and a standard
deviation, s, of 11.7 lb. Determine a 90% confidence interval for the standard deviation, , of the
weights of all men from this town.
101)
A)
8.7 to 16.5 lb
B)
8.9 to 17.4 lb
C)
9.5 to 2.7 lb
D)
9.2 to 15.1 lb
Answer Key
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Answer Key
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Answer Key
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