Download Chapter 6 - More on confidence intervals

Chapter 6 - More on confidence intervals
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the requested value.
1) A long-distance phone company wishes to estimate the mean duration of long-distance calls
originating in California. A random sample of 15 long-distance calls originating in California
yields the following call durations, in minutes.
5
15
1
4
14
19
4
20
12
1
40
2
1)
3
20
37
Use the data to obtain a point estimate of the mean call duration for all long-distance calls
originating in California.
A) 13.6 minutes
B) 13.3 minutes
C) 13.9 minutes
D) 13.1 minutes
Provide an appropriate response.
2) In stating a confidence-interval estimate of a population mean, the level of confidence increases as
the size of the interval
.
A) increases
2)
B) decreases
3) Is it true that the point estimate of a population mean must lie within the range of values defined
by the corresponding confidence-interval estimate, regardless of the level of confidence achieved?
Explain.
3)
A) No. The confidence interval only defines a range of values that is likely to contain the point
estimate with some prescribed level of confidence. This range of values is not guaranteed to
contain the point estimate.
B) Yes. By definition, the prescribed confidence interval contains the value of the point estimate.
Solve the problem.
4) Find the value of a that corresponds to a level of confidence of 93%.
A) 0.93
B) 7
C) 0.007
4)
D) 0.07
5) Find the level of confidence that corresponds to a value of a of 0.15.
A) 0.85%
B) 15%
C) 85%
5)
D) 0.075%
Find the confidence interval specified.
6) 48 packages are randomly selected from packages received by a parcel service. The sample has a
mean weight of 18.6 pounds. Assume that s = 3.4 pounds. What is the 95% confidence interval for
the true mean weight, m, of all packages received by the parcel service?
A) 17.8 to 19.4 pounds
B) 17.6 to 19.6 pounds
C) 17.3 to 19.9 pounds
D) 17.5 to 19.7 pounds
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6)
Provide an appropriate response.
7) Suppose you have obtained a 95% confidence interval for m. Which of the following statements
is/are true regarding the relationship between precision and confidence level? Assume that the
sample size is fixed.
A.
B.
C.
D.
7)
Increasing the confidence level to 99% will result in a narrower interval.
Decreasing the confidence level to 90% will result in greater precision.
Decreasing the precision will result in a higher confidence level.
Increasing the precision will result in a higher confidence level.
A) B and C
B) B and D
C) A and D
D) A and C
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
8) Mary wishes to estimate the mean height of women aged 18-24.She picks a sample of 100
women aged between 18 and 24 and constructs a 99% confidence interval for the
population mean. If she were to repeat this procedure 200 times in total, she would obtain
200 different confidence intervals. How many of these intervals would you expect to
8)
contain the population mean, m? Explain your thinking.
9) A psychologist wishes to estimate the mean IQ of students at one college. He picks a
random sample of 49 students from the college, measures each student's IQ, and obtains
9)
the following 95% confidence interval for the population mean, m: 115 to 125.How would
you interpret this confidence interval?
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine the margin of error in estimating the population mean,
m.
10) A telephone company wishes to estimate the mean duration of local calls. Given that
s = 3.0 minutes and that the sample size is 540, find the margin of error in estimating m at the 88%
level of confidence.
A) 0.083 minutes
B) 0.009 minutes
C) 0.005 minutes
10)
D) 0.201 minutes
11) Based on a sample of 34 randomly selected years, a 90% confidence interval for the mean annual
precipitation in one city is from 47.5 inches to 50.5 inches. Find the margin of error.
11)
A) 3 inches
B) 1.5 inches
C) There is not enough information to find the margin of error.
D) 0.42
Find the necessary sample size.
12) Weights of women in one age group are normally distributed with a standard deviation s of 15 lb.
A researcher wishes to estimate the mean weight of all women in this age group. Find how large a
sample must be drawn in order to be 90 percent confident that the sample mean will not differ
from the population mean by more than 3.0 lb.
A) 69
B) 68
C) 97
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D) 66
12)
13) Scores on a certain test are normally distributed with a variance of 77. A researcher wishes to
estimate the mean score achieved by all adults on the test. Find the sample size needed to assure
with 95.44 percent confidence that the sample mean will not differ from the population mean by
more than 3 units.
A) 12
B) 103
C) 35
D) 2636
14) You wish to estimate the mean weight of machine components of a certain type and you require a
96% degree of confidence that the sample mean will be in error by no more than 0.009 g. After
using the range rule of thumb to estimate the standard deviation, find the sample size required.
Typical weights range from 8.35 g to 8.63 g.
A) 186
B) 16
C) 255
13)
14)
D) 14
Provide an appropriate response.
15) Suppose you have obtained a confidence interval for m, but wish to obtain a greater degree of
precision. Which of the following would result in a narrower confidence interval?
15)
A. Increasing the sample size while keeping the confidence level fixed
B. Decreasing the sample size while keeping the confidence level fixed
C. Increasing the confidence level while keeping the sample size fixed
D. Decreasing the confidence level while keeping the sample size fixed
A) A and D
B) B and D
C) A and C
D) B and C
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
16) A researcher estimates that the mean systolic blood pressure for women aged between 18
and 24 is 118 mmHg. At the 95% confidence level, the margin of error is 2.4 mmHg. How
would you interpret this margin of error?
16)
17) A sample mean is used to esimate a population mean. To obtain a margin of error of 1.5 at
a confidence level of 95%, a sample size of 120 is needed. Would the required sample size
be larger or smaller if the researcher wished to
17)
(a) increase the confidence level while keeping the same margin of error?
(b) decrease the margin of error while keeping the same confidence level?
Explain your answers.
18) Based on a sample of size 25, a researcher obtains an estimate of 64.4 inches for the mean
height of all women aged 30-40. At the 95% confidence level, the margin of error is
1.2 inches. Do you agree with the interpretation below? If not, explain why not and give a
correct interpretation.
Researcher's interpretation: "We can be 95% confident that the height of a randomly
selected woman will differ from 64.4 inches by at most 1.2 inches."
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18)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the necessary sample size.
19) The weekly earnings of students in one age group are normally distributed with a standard
deviation of 36 dollars. A researcher wishes to estimate the mean weekly earnings of students in
this age group. Find the sample size needed to assure with 98 percent confidence that the sample
mean will not differ from the population mean by more than 3 dollars.
A) 11
B) 22
C) 782
19)
D) 66
Find the confidence interval specified.
20) A random sample of 93 light bulbs had a mean life of x = 489 hours. Assume that s = 28 hours.
Construct a 90% confidence interval for the mean life, m, of all light bulbs of this type.
A) 483.3 to 494.7 hours
B) 481.5 to 496.5 hours
C) 482.2 to 495.8 hours
D) 484.2 to 493.8 hours
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20)
Answer Key
Testname: MORE-CHAPTER6
1)
2)
3)
4)
5)
6)
7)
8)
D
A
B
D
C
B
A
Approximately 198 of the intervals will contain the population mean. The chance that any given confidence interval
contains the true mean is 99%, so out of 200 such confidence intervals approximately 99% of 200, or 198, intervals will
contain m.
9) We can be 95% confident that the mean IQ of all students at the college is somewhere between 115 and 125.
10)
11)
12)
13)
14)
15)
16)
17)
D
B
B
C
C
A
The researcher is 95% confident that the estimate of 118 mmHg differs from the true mean by at most 2.4 mmHg.
In both cases, a larger sample would be needed.
18) The researcher's interpretation is not correct since the margin of error refers to the difference between the estimate and
the true mean, not to the difference between the estimate and the height of an individual woman. The correct
interpretation is: We can be 95% confident that the estimate of 64.4 inches differs from the true mean by at most
1.2 inches.
19) C
20) D
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