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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the given data to find the minimum sample size required to estimate the population proportion.
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1) Margin of error: 0.07; confidence level: 95%; from a prior study, p is estimated by the decimal
equivalent of 92%.
A) 58
B) 4
C) 174
D) 51
1)
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
2) 95% confidence; the sample size is 9900, of which 30% are successes
2)
A) 0.00903
B) 0.00677
C) 0.0104
D) 0.0119
Find the appropriate minimum sample size.
3) You want to be 95% confident that the sample variance is within 40% of the population variance.
A) 224
B) 57
C) 11
D) 14
3)
Do one of the following, as appropriate: (a) Find the critical value z /2, (b) find the critical value t /2, (c) state that
neither the normal nor the t distribution applies.
4) 91%; n = 45; is known; population appears to be very skewed.
4)
A) z /2 = 1.70
B) t /2 = 1.645
C) t /2 = 1.34
D) z /2 = 1.75
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
5) In a random sample of 192 college students, 129 had part-time jobs. Find the margin of error for
5)
the 95% confidence interval used to estimate the population proportion.
A) 0.00225
B) 0.116
C) 0.0598
D) 0.0664
Use the given information to find the minimum sample size required to estimate an unknown population mean µ.
6) How many women must be randomly selected to estimate the mean weight of women in one age
6)
group. We want 90% confidence that the sample mean is within 3.4 lb of the population mean, and
the population standard deviation is known to be 25 lb.
A) 145
B) 208
C) 147
D) 148
Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume
that the population has a normal distribution.
7) The principal randomly selected six students to take an aptitude test. Their scores were:
7)
88.0 84.1 74.9 83.2 83.7 85.5
Determine a 90% confidence interval for the mean score for all students.
A) 79.59 < µ < 86.88
B) 79.49 < µ < 86.98
C) 86.88 < µ < 79.59
D) 86.98 < µ < 79.49
Provide an appropriate response.
8) The confidence interval, 3.56 <
< 5.16, for the population standard deviation is based on the
following sample statistics: n = 41, x = 30.8, and s = 4.2. What is the degree of confidence?
A) 95%
B) 80%
C) 90%
D) 99%
1
8)
Solve the problem.
9) A 99% confidence interval (in inches) for the mean height of a population is 65.7 < µ < 67.3. This
result is based on a sample of size 144. Construct the 95% confidence interval. (Hint: you will first
need to find the sample mean and sample standard deviation).
A) 66.0 in < µ < 67.0 in.
B) 65.6 in < µ < 67.4 in.
C) 65.7 in < µ < 67.3 in.
D) 65.9 in < µ < 67.1 in.
10) Find the critical value
A) 12.833
2
R corresponding to a sample size of 6 and a confidence level of 95 percent.
B) 11.07
C) 1.145
9)
10)
D) 0.831
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .
Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place
than is used for the original set of data.
11) The daily intakes of milk (in ounces) for ten randomly selected people were:
11)
23.3 28.4 10.5 16.4 26.4
18.1 20.4 17.3 27.4 13.2
Find a 99% confidence interval for the population standard deviation .
A) 3.66 oz < < 12.53 oz
B) 0.88 oz < < 3.38 oz
C) 3.78 oz < < 12.53 oz
D) 3.78 oz < < 13.95 oz
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
12) A survey of 300 union members in New York State reveals that 112 favor the Republican candidate
12)
for governor. Construct the 98% confidence interval for the true population proportion of all New
York State union members who favor the Republican candidate.
A) 0.308 < p < 0.438
B) 0.301 < p < 0.445
C) 0.304 < p < 0.442
D) 0.316 < p < 0.430
Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your
answer to the same number of decimal places as the sample mean.
13) A random sample of 104 light bulbs had a mean life of x = 543 hours with a standard deviation of
= 26 hours. Construct a 90% confidence interval for the mean life, µ, of all light bulbs of this
type.
A) 536 hr < µ < 550 hr
B) 538 hr < µ < 548 hr
C) 537 hr < µ < 549 hr
D) 539 hr < µ < 547 hr
13)
14) A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of
5.2 on a placement test. What is the 90% confidence interval for the mean score, µ, of all students
taking the test?
A) 27.8 < µ < 31.2
B) 28.4 < µ < 30.6
C) 27.9 < µ < 31.1
D) 28.2 < µ < 30.8
14)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
15) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. 15)
Construct the 95% confidence interval for the true proportion of all voters in the state who favor
approval.
A) 0.471 < p < 0.472
B) 0.435 < p < 0.508
C) 0.444 < p < 0.500
D) 0.438 < p < 0.505
2
Solve the problem.
16) Find the chi-square value
percent.
A) 0.216
2
L corresponding to a sample size of 4 and a confidence level of 98
B) 9.348
C) 0.115
16)
D) 11.345
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .
Assume that the population has a normal distribution. Round the confidence interval limits to the same number of
decimal places as the sample standard deviation.
17) College students' annual earnings: 98% confidence; n = 9, x = $3361, s = $865
A) $584 < < $1657
B) $526 < < $1693
C) $681 < < $1128
D) $546 < < $1907
17)
Use the given information to find the minimum sample size required to estimate an unknown population mean µ.
18) How many weeks of data must be randomly sampled to estimate the mean weekly sales of a new
18)
line of athletic footwear? We want 98% confidence that the sample mean is within $400 of the
population mean, and the population standard deviation is known to be $1400.
A) 82
B) 34
C) 67
D) 48
Use the given data to find the minimum sample size required to estimate the population proportion.
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19) Margin of error: 0.028; confidence level: 99%; p and q unknown
A) 1939
B) 2115
C) 1116
D) 2223
19)
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
20) 98% confidence; the sample size is 800, of which 40% are successes
20)
A) 0.0339
B) 0.0355
C) 0.0446
D) 0.0404
Use the given data to find the minimum sample size required to estimate the population proportion.
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21) Margin of error: 0.008; confidence level: 98%; p and q unknown
A) 20,308
B) 22,184
C) 21,207
D) 10,384
21)
Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your
answer to the same number of decimal places as the sample mean.
22) 37 packages are randomly selected from packages received by a parcel service. The sample has a
22)
mean weight of 10.3 pounds and a standard deviation of 2.4 pounds. What is the 95% confidence
interval for the true mean weight, µ, of all packages received by the parcel service?
A) 9.6 lb < µ < 11.0 lb
B) 9.3 lb < µ < 11.3 lb
C) 9.5 lb < µ < 11.1 lb
D) 9.4 lb < µ < 11.2 lb
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .
Assume that the population has a normal distribution. Round the confidence interval limits to the same number of
decimal places as the sample standard deviation.
23) The mean replacement time for a random sample of 20 washing machines is 10.9 years and the
23)
standard deviation is 2.7 years. Construct a 99% confidence interval for the standard deviation, ,
of the replacement times of all washing machines of this type.
A) 1.9 yr < < 4.5 yr
B) 1.9 yr < < 5.7 yr
C) 1.8 yr < < 5.1 yr
D) 2.0 yr < < 4.3 yr
3
Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume
that the population has a normal distribution.
24) A savings and loan association needs information concerning the checking account balances of its
24)
local customers. A random sample of 14 accounts was checked and yielded a mean balance of
$664.14 and a standard deviation of $297.29. Find a 98% confidence interval for the true mean
checking account balance for local customers.
A) $492.52 < µ < $835.76
B) $493.71 < µ < $834.57
C) $453.59 < µ < $874.69
D) $455.65 < µ < $872.63
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .
Assume that the population has a normal distribution. Round the confidence interval limits to the same number of
decimal places as the sample standard deviation.
25) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly
25)
selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct the 95% confidence interval for the standard deviation, , of the scores of all subjects.
A) 17.2 < < 27.2
B) 16.6 < < 28.6
C) 16.9 < < 29.3
D) 17.5 < < 27.8
Find the appropriate minimum sample size.
26) To be able to say with 95% confidence level that the standard deviation of a data set is within 10%
of the population's standard deviation, the number of observations within the data set must be
greater than or equal to what quantity?
A) 250
B) 805
C) 335
D) 192
26)
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .
Assume that the population has a normal distribution. Round the confidence interval limits to the same number of
decimal places as the sample standard deviation.
27) To find the standard deviation of the diameter of wooden dowels, the manufacturer measures 19
27)
randomly selected dowels and finds the standard deviation of the sample to be s = 0.16. Find the
95% confidence interval for the population standard deviation .
A) 0.11 < < 0.25
B) 0.13 < < 0.22
C) 0.15 < < 0.21
D) 0.12 < < 0.24
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
28) Of 150 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence
28)
interval for the true percentage of all adults in the town that smoke.
A) 14.6% < p < 25.4%
B) 11.6% < p < 28.4%
C) 12.4% < p < 27.6%
D) 13.6% < p < 26.4%
Solve the problem.
29) The following confidence interval is obtained for a population proportion, p: (0.688, 0.724). Use
29)
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these confidence interval limits to find the point estimate, p.
A) 0.724
B) 0.706
C) 0.688
D) 0.708
Use the given data to find the minimum sample size required to estimate the population proportion.
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30) Margin of error: 0.04; confidence level: 99%; from a prior study, p is estimated by 0.12.
A) 438
B) 254
C) 18
D) 526
4
30)
Solve the problem. Round the point estimate to the nearest thousandth.
31) 50 people are selected randomly from a certain population and it is found that 12 people in the
sample are over 6 feet tall. What is the point estimate of the proportion of people in the population
who are over 6 feet tall?
A) 0.76
B) 0.24
C) 0.50
D) 0.18
Solve the problem.
32) The following confidence interval is obtained for a population proportion, p: 0.753 < p < 0.797. Use
31)
32)
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these confidence interval limits to find the point estimate, p.
A) 0.753
B) 0.780
C) 0.775
D) 0.770
Use the given information to find the minimum sample size required to estimate an unknown population mean µ.
33) How many students must be randomly selected to estimate the mean weekly earnings of students
33)
at one college? We want 95% confidence that the sample mean is within $2 of the population mean,
and the population standard deviation is known to be $60.
A) 3047
B) 3458
C) 4886
D) 2435
Use the given data to find the minimum sample size required to estimate the population proportion.
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34) Margin of error: 0.04; confidence level: 95%; from a prior study, p is estimated by the decimal
equivalent of 60%.
A) 519
B) 1441
C) 996
D) 577
34)
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
35) 95% confidence; n = 2388, x = 1672
35)
A) 0.0184
B) 0.0248
C) 0.0206
D) 0.0156
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
36) A study involves 607 randomly selected deaths, with 35 of them caused by accidents. Construct a
36)
98% confidence interval for the true percentage of all deaths that are caused by accidents.
A) 4.20% < p < 7.33%
B) 3.33% < p < 8.21%
C) 3.56% < p < 7.97%
D) 3.91% < p < 7.62%
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .
Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place
than is used for the original set of data.
37) The football coach randomly selected ten players and timed how long each player took to perform
37)
a certain drill. The times (in minutes) were:
9 7 15 6 15
12 8 6 14 5
Find a 95% confidence interval for the population standard deviation .
A) 2.7 min < < 6.6 min
B) 2.6 min < < 6.6 min
C) 2.7 min < < 7.2 min
D) 0.8 min < < 2.4 min
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to four decimal places.
38) In a clinical test with 1600 subjects, 800 showed improvement from the treatment. Find the margin
38)
of error for the 99% confidence interval used to estimate the population proportion.
A) 0.0282
B) 0.0245
C) 0.0184
D) 0.0322
5
Solve the problem.
39) When obtaining a confidence interval for a population mean in the case of a finite population of
size N and a sample size n which is greater than 0.05N, the margin of error is multiplied by the
following finite population correction factor:
39)
N-n
N-1
Find the 95% confidence interval for the mean of 200 weights if a sample of 34 of those weights
yields a mean of 155.7 lb and a standard deviation of 24.1 lb.
A) 149.3 lb < µ < 162.1 lb
B) 147.6 lb < µ < 163.8 lb
C) 148.3 lb < µ < 163.1 lb
D) 146.8 lb < µ < 164.6 lb
40) Suppose that n trials of a binomial experiment result in no successes. According to the "Rule of
Three", we have 95% confidence that the true population proportion has an upper bound of 3/n. If a
manufacturer randomly selects 25 computers for quality control and finds no defective computers,
what statement can you make by using the rule of three, about the proportion p, of all its
computers which are defective?
1
3
and
.
A) We are 95% confident that p lies between
25
25
B) We are 95% confident that p does not exceed
C) The value of p cannot be greater than
3
.
25
3
.
25
D) We are 95% confident that p is greater than
3
.
25
Find the indicated critical z value.
41) Find the value of z /2 that corresponds to a confidence level of 89.48%.
A) -1.62
40)
B) 1.25
C) 0.0526
41)
D) 1.62
Find the appropriate minimum sample size.
42) You want to be 99% confident that the sample standard deviation s is within 5% of the population
standard deviation.
A) 2638
B) 1336
C) 2434
D) 923
42)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
43) n = 85, x = 49; 98% confidence
43)
A) 0.471 < p < 0.681
B) 0.470 < p < 0.682
C) 0.451 < p < 0.701
D) 0.450 < p < 0.702
Solve the problem.
44) A 99% confidence interval (in inches) for the mean height of a population is 65.92 < µ < 67.48. This
result is based on a sample of size 144. If the confidence interval 66.13 < µ < 67.27 is obtained from
the same sample data, what is the degree of confidence? (Hint: you will first need to find the
sample mean and sample standard deviation).
A) 92%
B) 93%
C) 95%
D) 94%
6
44)
Use the given data to find the minimum sample size required to estimate the population proportion.
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45) Margin of error: 0.005; confidence level: 97%; p and q unknown
A) 37,127
B) 47,180
C) 47,089
D) 46,570
45)
Provide an appropriate response.
46) The confidence interval, 17.12 < 2 < 78.88, for the population variance is based on the following
46)
sample statistics: n = 25, x = 42.6 and s = 5.7. What is the degree of confidence?
A) 95%
B) 90%
C) 98%
D) 99%
Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume
that the population has a normal distribution.
47) n = 12, x = 23.6, s = 6.6, 99% confidence
A) 17.70 < µ < 29.50
C) 18.42 < µ < 28.78
47)
B) 17.56 < µ < 29.64
D) 17.68 < µ < 29.52
Use the given data to find the minimum sample size required to estimate the population proportion.
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48) Margin of error: 0.005; confidence level: 96%; p and q unknown
A) 32,024
B) 42,018
C) 42,148
D) 42,025
48)
Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume
that the population has a normal distribution.
49) n = 30, x = 84.6, s = 10.5, 90% confidence
A) 79.32 < µ < 89.88
C) 81.36 < µ < 87.84
B) 80.68 < µ < 88.52
D) 81.34 < µ < 87.86
49)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
50) Of 346 items tested, 12 are found to be defective. Construct the 98% confidence interval for the
50)
proportion of all such items that are defective.
A) 0.0118 < p < 0.0576
B) 0.0154 < p < 0.0540
C) 0.0110 < p < 0.0584
D) 0.0345 < p < 0.0349
Solve the problem.
51) The following confidence interval is obtained for a population proportion, p: (0.399, 0.437). Use
these confidence interval limits to find the margin of error, E.
A) 0.019
B) 0.038
C) 0.017
D) 0.020
51)
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation .
Assume that the population has a normal distribution. Round the confidence interval limits to one more decimal place
than is used for the original set of data.
52) The amounts (in ounces) of juice in eight randomly selected juice bottles are:
52)
15.2 15.1 15.9 15.5
15.6 15.1 15.8 15.0
Find a 98% confidence interval for the population standard deviation .
A) 0.21 oz < < 0.71 oz
B) 0.20 oz < < 0.71 oz
C) 0.21 oz < < 0.82 oz
D) 0.22 oz < < 0.86 oz
7
Solve the problem.
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53) A one-sided confidence interval for p can be written as p < p + E or p > p - E where the margin of
error E is modified by replacing z /2 with z . If a teacher wants to report that the fail rate on a test
is at most x with 90% confidence, construct the appropriate one-sided confidence interval. Assume
that a simple random sample of 74 students results in 8 who fail the test.
A) p > 0.062
B) p < 0.154
C) p < 0.062
D) p < 0.167
53)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
54) n = 109, x = 65; 88% confidence
54)
A) 0.523 < p < 0.669
B) 0.519 < p < 0.673
C) 0.518 < p < 0.674
D) 0.522 < p < 0.670
Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume
that the population has a normal distribution.
55) The amounts (in ounces) of juice in eight randomly selected juice bottles are:
55)
15.4 15.8 15.4 15.1
15.8 15.9 15.8 15.7
Construct a 98% confidence interval for the mean amount of juice in all such bottles.
A) 15.99 oz < µ < 15.23 oz
B) 15.23 oz < µ < 15.99 oz
C) 15.89 oz < µ < 15.33 oz
D) 15.33 oz < µ < 15.89 oz
Solve the problem. Round the point estimate to the nearest thousandth.
56) 445 randomly selected light bulbs were tested in a laboratory, 316 lasted more than 500 hours. Find
a point estimate of the proportion of all light bulbs that last more than 500 hours.
A) 0.708
B) 0.710
C) 0.290
D) 0.415
56)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
57) Of 260 employees selected randomly from one company, 18.46% of them commute by carpooling.
57)
Construct a 90% confidence interval for the true percentage of all employees of the company who
carpool.
A) 14.5% < p < 22.4%
B) 12.9% < p < 24.1%
C) 12.3% < p < 24.7%
D) 13.7% < p < 23.2%
Use the given information to find the minimum sample size required to estimate an unknown population mean µ.
58) Margin of error: $135, confidence level: 95%, = $500
58)
A) 46
B) 53
C) 37
D) 74
Do one of the following, as appropriate: (a) Find the critical value z /2, (b) find the critical value t /2, (c) state that
neither the normal nor the t distribution applies.
59) 90%; n =9; = 4.2; population appears to be very skewed.
59)
A) z /2 = 2.365
B) Neither the normal nor the t distribution applies.
C) z /2 = 2.896
D) z /2 = 2.306
Express the confidence interval using the indicated format.
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60) Express the confidence interval 0.38 < p < 0.54 in the form of p ± E.
A) 0.46 ± 0.08
B) 0.38 ± 0.16
C) 0.38 ± 0.08
8
D) 0.46 ± 0.16
60)
Answer Key
Testname: TEST 3
1) A
2) A
3) B
4) A
5) D
6) C
7) A
8) C
9) D
10) A
11) D
12) A
13) D
14) B
15) D
16) C
17) D
18) C
19) B
20) D
21) C
22) C
23) A
24) C
25) C
26) D
27) D
28) B
29) B
30) A
31) B
32) C
33) B
34) D
35) A
36) C
37) C
38) D
39) C
40) B
41) D
42) B
43) C
44) D
45) C
46) D
47) D
48) D
49) D
50) A
9
Answer Key
Testname: TEST 3
51) A
52) C
53) B
54) A
55) D
56) B
57) A
58) B
59) B
60) A
10