Chapter 7 - Practice Problems 1
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
1) Define a point estimate. What is the best point estimate for µ?
1)
2) Define margin of error. Explain the relation between the confidence interval and the error
2)
estimate. Suppose a confidence interval is 9.65 < µ < 11.35. Find the sample mean x and the
error estimate E.
3) How do you determine whether to use the z or t distribution in computing the margin of
s
error, E = z
or E = t
?
·
·
/2
/2
n
n
3)
4) When determining the sample size needed to achieve a particular error estimate you need
to know . What are two methods of estimating if is unknown?
4)
5) Interpret the following 95% confidence interval for mean weekly salaries of shift managers
at Guiseppe's Pizza and Pasta.
325.80 < µ < 472.30
5)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
6) Find the critical value z /2 that corresponds to a degree of confidence of 98%.
A) 2.575
B) 2.05
C) 2.33
6)
D) 1.75
7) Find the critical value z /2 that corresponds to a degree of confidence of 91%.
A) 1.75
B) 1.70
C) 1.645
7)
D) 1.34
^
Express the confidence interval in the form of p ± E.
8) -0.134 < p < 0.666
^
A) p = 0.266 - 0.4
8)
^
^
B) p = 0.4 ± 0.5
C) p = 0.266 ± 0.5
1
^
D) p = 0.266 ± 0.4
Solve the problem.
9) The following confidence interval is obtained for a population proportion, p:
(0.700, 0.728)
9)
^
Use these confidence interval limits to find the point estimate, p .
A) 0.718
B) 0.714
C) 0.728
D) 0.700
10) The following confidence interval is obtained for a population proportion, p:
0.478 < p < 0.510
Use these confidence interval limits to find the margin of error, E.
A) 0.032
B) 0.016
C) 0.494
10)
D) 0.017
Find the margin of error for the 95% confidence interval used to estimate the population proportion.
11) n = 151, x = 122
A) 0.110
B) 0.00201
C) 0.0628
D) 0.0565
12) In a survey of 4800 T.V. viewers, 50% said they watch network news programs.
A) 0.0141
B) 0.0106
11)
C) 0.0162
12)
D) 0.0185
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
13) n = 54, x = 13; 95 percent
13)
A) 0.144 < p < 0.338
C) 0.145 < p < 0.337
B) 0.126 < p < 0.356
D) 0.127 < p < 0.355
14) n = 140, x = 81; 90 percent
14)
A) 0.514 < p < 0.644
C) 0.510 < p < 0.648
B) 0.509 < p < 0.649
D) 0.513 < p < 0.645
^
Find the minimum sample size you should use to assure that your estimate of p will be within the required margin of
error around the population p.
15) Margin of error: 0.012; confidence level: 93%; p and q unknown
A) 5700
B) 1
C) 38
D) 5701
16) Margin of error: 0.006; confidence level: 97%; p and q unknown
A) 197
B) 32,704
C) 196
D) 32,702
15)
16)
17) Margin of error: 0.07; confidence level: 90%; from a prior study, p is estimated by 0.22.
A) 285
B) 84
C) 7
D) 95
17)
18) Margin of error: 0.03; confidence level: 95%; from a prior study, p is estimated by the decimal
equivalent of 58%.
A) 1040
B) 1795
C) 936
D) 2476
18)
2
Solve the problem.
19) Find the point estimate of the true proportion of people who wear hearing aids if, in a random
sample of 496 people, 73 people had hearing aids.
A) 0.128
B) 0.853
C) 0.147
D) 0.145
20) 50 people are selected randomly from a certain population and it is found that 13 people in the
sample are over 6 feet tall. What is the point estimate of the true proportion of people in the
population who are over 6 feet tall?
A) 0.50
B) 0.74
C) 0.26
19)
20)
D) 0.19
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
21) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.
Construct the 95% confidence interval for the true proportion of all voters in the state who favor
approval.
A) 0.438 < p < 0.505
C) 0.471 < p < 0.472
21)
B) 0.444 < p < 0.500
D) 0.435 < p < 0.508
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
22) Of 99 adults selected randomly from one town, 63 have health insurance. Find a 90% confidence
22)
interval for the true proportion of all adults in the town who have health insurance.
A) 0.542 < p < 0.731
C) 0.557 < p < 0.716
B) 0.524 < p < 0.749
D) 0.512 < p < 0.761
23) Of 112 randomly selected adults, 34 were found to have high blood pressure. Construct a 95%
confidence interval for the true percentage of all adults that have high blood pressure.
A) 19.1% < p < 41.6%
C) 21.8% < p < 38.9%
B) 23.2% < p < 37.5%
D) 20.2% < p < 40.5%
Solve the problem.
24)
Find the critical value z /2 that corresponds to a degree of confidence of 91%.
A) 1.75
23)
B) 1.645
C) 1.34
24)
D) 1.70
Determine whether the given conditions justify using the margin of error E = z /2 / n when finding a confidence
interval estimate of the population mean µ.
25) The sample size is n = 205 and
25)
= 15.
A) Yes
26) The sample size is n = 12,
B) No
is not known, and the original population is normally distributed.
A) Yes
B) No
3
26)
Use the confidence level and sample data to find the margin of error E.
27) Weights of eggs: 95% confidence; n = 52, x = 1.78 oz,
A) 0.02 oz
B) 0.11 oz
= 0.40 oz
C) 0.09 oz
27)
D) 7.21 oz
28) Systolic blood pressures for women aged 18-24: 94% confidence; n = 98, x = 113.1 mm Hg,
= 13.4 mm Hg
A) 50.3 mm Hg
B) 9.9 mm Hg
C) 2.2 mm Hg
28)
D) 2.5 mm Hg
Use the confidence level and sample data to find a confidence interval for estimating the population µ.
29) Test scores: n = 95, x = 73.8,
= 7.4; 99 percent
A) 72.5 < µ < 75.1
B) 71.8 < µ < 75.8
29)
C) 72.3 < µ < 75.3
D) 72.0 < µ < 75.6
30) A random sample of 194 full-grown lobsters had a mean weight of 21 ounces and a standard
deviation of 3.8 ounces. Construct a 98 percent confidence interval for the population mean µ.
A) 20 < µ < 23
B) 21 < µ < 23
C) 20 < µ < 22
Use the margin of error, confidence level, and standard deviation
an unknown population mean µ.
31) Margin of error: $124, confidence level: 95%,
A) 62
D) 19 < µ < 21
to find the minimum sample size required to estimate
31)
= $530
B) 2
30)
C) 5
D) 71
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.
32) 98%; n = 7;
A) z /2 = 2.33
33) 99%; n = 17;
B) t /2 = 1.96
C) t /2 = 2.575
D) z /2 = 2.05
33)
is unknown; population appears to be normally distributed.
A) t /2 = 2.921
34) 95%; n = 11;
32)
= 27; population appears to be normally distributed.
B) t /2 = 2.898
C) z /2 = 2.567
is known; population appears to be very skewed.
A) z /2 = 1.812
B) Neither the normal nor the t distribution applies.
C) z /2 = 1.96
D) t /2 = 2.228
4
D) z /2 = 2.583
34)
Find the margin of error.
_
35) 95% confidence interval; n = 91 ; x = 53, s = 12.5
A) 2.60
35)
B) 4.80
C) 2.23
D) 2.34
_
36) 95% confidence interval; n = 51; x = 129; s = 274
A) 100.2
36)
B) 77.1
C) 69.4
D) 161.9
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.
37) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 208
37)
milligrams with s = 18.2 milligrams. Construct a 95 percent confidence interval for the true mean
cholesterol content of all such eggs.
A) 196.4 < µ < 219.6
C) 196.3 < µ < 219.7
B) 198.6 < µ < 217.4
D) 196.5 < µ < 219.5
38) A sociologist develops a test to measure 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 the 95% confidence interval for the mean score of all such subjects.
A) 74.6 < µ < 77.8
B) 67.7 < µ < 84.7
C) 64.2 < µ < 88.2
5
D) 69.2 < µ < 83.2
38)
Answer Key
Testname: CH 7 SET 1
1) A point estimate is a single value used to approximate a population parameter. The sample mean x is the best point
estimate of μ.
2) The margin of error is the maximum likely difference between the observed sample mean x and the true value for the
population mean μ. The confidence interval is found by taking the sample mean x and adding the margin of error E to
find the high value and subtracting E to find the low value of the interval. In the interval 9.65 < μ < 11.35, the sample
mean x is 10.5 and the error estimate E is 0.85.
3) Provided n > 30, the standard normal distribution is the one to use. If n ≤ 30, the population must be normal and σ
must be known to use the formula.
4) 1) Use the range rule of thumb.
2) Conduct a pilot study and base your estimate of σ on the first collection of at least 31 randomly selected values.
5) We are 95% sure that the interval contains the true population value for mean weekly salaries of shift managers at
Guiseppeʹs Pizza and Pasta.
6) C
7) B
8) D
9) B
10) B
11) C
12) A
13) D
14) C
15) D
16) B
17) D
18) A
19) C
20) C
21) A
22) C
23) C
24) D
25) A
26) B
27) B
28) D
29) B
30) C
31) D
32) A
33) A
34) B
35) A
36) B
37) A
38) B
6