1. Estimation is a procedure by which we assign a numerical value or numerical values to
the:
A) population parameter based on the information collected from a sample
B) sample statistic based on the information collected from a sample
C) population parameter based on the information collected from a population
D) sample statistic based on the information collected from a population
2. The values assigned to a population parameter based on the value(s) of a sample statistic
are:
A) the probabilities C) a sampling distribution
B) the probability distribution D) estimate(s)
3. The sample statistic used to estimate a population parameter is a(n):
A) random variable B) qualitative variable C) estimator D) parameter
4. The single value of a sample statistic that we assign to the population parameter is a:
A) single estimate B) unique estimate C) point estimate D) singular
estimate
5. The confidence level of an interval estimate is denoted by:
A)
B)
( )
1 100%
−
C)
D)
( )
1 100%
−
6. For most distributions, we can use the normal distribution to make a confidence interval
for a population mean provided that the population standard deviation
is known and
the sample size is:
A) greater than 30 C) greater than or equal to 30
B) less than 25 D) greater than 100
7. The margin of error for the population mean, assuming
is known, is:
A) z multiplied by the population standard deviation
B) z multiplied by t
C) z multiplied by the standard deviation of the sample mean
D) z multiplied by the sample mean
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8. The z value for a 90% confidence interval for the population mean with
known is:
A) 2.05 B) 1.645 C) 2.17 D) 1.60
9. The z value for a 85% confidence interval for the population mean with
known is:
A) 1.96 B) 2.33 C) 1.44 D) 2.58
10. The width of a confidence interval depends on the size of the:
A) population mean B) margin of error C) sample mean D) none of these
11. You can decrease the width of a confidence interval by:
A) lowering the confidence level or decreasing the sample size
B) increasing the confidence level or decreasing the sample size
C) lowering the confidence level or increasing the sample size
D) increasing the confidence level or increasing the sample size
12. To decrease the width of a confidence interval, we should always prefer to:
A) lower the confidence level C) increase the sample size
B) increase the confidence level D) decrease the sample size
13. A sample of size 97 from a population having standard deviation
= 7 produced a
mean of 47. The 99% confidence interval for the population mean (rounded to two
decimal places) is:
14. A sample of size 65 from a population having standard deviation
= 55 produced a
mean of 234.00. The 95% confidence interval for the population mean (rounded to two
decimal places) is:
Chapter 8
15. A random sample of 82 customers, who visited a department store, spent an average of
$71 at this store. Suppose the standard deviation of expenditures at this store is
= $19.
The 98% confidence interval for the population mean (rounded to two decimal places) is:
16. The mean IQ score of a sample of 61 students selected from a high school is 87. Suppose
the standard deviation of IQ’s at this school is
= 8.4. The 99% confidence interval
for the population mean (rounded to two decimal places) is:
17. The mean federal income tax paid last year by a random sample of 45 persons selected
from a city was $4,242. Suppose the standard deviation of tax paid in this city is
=
$991. The 95% confidence interval for the population mean (rounded to two decimal
places) is:
18. We use the t distribution to make a confidence interval for the population mean if the
population from which the sample is drawn is (approximately) normally distributed, the
population standard deviation is unknown, and the sample size is at least:
A) 30 B) 100 C) 50 D) 2
19. Which of the following conditions is required to use the t distribution to make a
confidence interval for the population mean?
A) The population from which the sample is drawn is (approximately) normally
distributed.
B) The sample size is at least 30.
C) The population from which the sample is drawn has a t distribution.
D) The population standard deviation is known.
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20. When making a confidence interval for the population mean using the t procedures, the
degrees of freedom for the t distribution are:
A) n B) n – 2 C) n + 1 D) n – 1
21. The value of t for 19 degrees of freedom and a 98% confidence interval is:
A) 2.861 B) 2.539 C) -2.539 D) 1.328
22. The value of t for 19 degrees of freedom and a 90% confidence interval is:
A) 1.729 B) -1.729 C) 2.539 D) -2.539
23. A sample of 20 elements produced a mean of 91.4 and a standard deviation of 11.16.
Assuming that the population has a normal distribution, the 90% confidence interval for
the population mean is:
24. A sample of 25 elements produced a mean of 123.4 and a standard deviation of 18.32.
Assuming that the population has a normal distribution, the 90% confidence interval for
the population mean, rounded to two decimal places, is:
25. A random sample of 23 tourists who visited Hawaii this summer spent an average of
$1,456.0 on this trip with a standard deviation of $263.00. Assuming that the money
spent by all tourists who visit Hawaii has an approximate normal distribution, the 95%
confidence interval for the average amount of money spent by all tourists who visit
Hawaii, rounded to two decimal places, is:
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26. A random sample of 12 life insurance policy holders showed that the mean value of their
life insurance policies is $210,000 with a standard deviation of $44,600. Assuming that
the values of life insurance policies for all such policy holders are approximately
normally distributed, the 99% confidence interval for the mean value of all life insurance
policies, rounded to two decimal places, is:
27. A random sample of 8 houses selected from a city showed that the mean size of these
houses is 1,881.0 square feet with a standard deviation of 328.00 square feet. Assuming
that the sizes of all houses in this city have an approximate normal distribution, the 90%
confidence interval for the mean size of all houses in this city, rounded to two decimal
places, is:
28. A random sample of 450 produced a sample proportion of 0.71. The 95% confidence
interval for the population proportion, rounded to four decimal places, is:
29. A random sample of 188 produced a sample proportion of 0.40. The 98% confidence
interval for the population proportion, rounded to four decimal places, is:
30. A random sample of 1,100 adults showed that 32% of them are smokers. Based on this
sample, the 90% confidence interval for the proportion of all adults who are smokers,
rounded to four decimal places, is:
Chapter 8
31. In a random sample of 562 items produced by a machine, the quality control staff found
6.6% to be defective. Based on this sample, the 95% confidence interval for the
proportion of defective items in all items produced by this machine, rounded to four
decimal places, is:
32. A random sample of 983 families selected from a large city showed that 17.5% of them
make $100,000 or more per year. Based on this sample, the 99% confidence interval for
the proportion of all families living in this city who make $100,000 or more per year,
rounded to four decimal places, is:
33. A random sample of 765 persons showed that 13.5% do not have any health insurance.
Based on this sample, the 95% confidence interval for the proportion of all persons who
do not have any health insurance, rounded to four decimal places, is:
34. A researcher wants to make a 99% confidence interval for a population mean. She wants
the margin of error to be within 4.6 of the population mean. The population standard
deviation is 18.22. The sample size that will yield a margin of error within 4.6 of the
population mean is:
35. A researcher wants to make a 95% confidence interval for a population mean. She
wants the margin of error to be within 1.9 of the population mean. The population
standard deviation is 11.07. The sample size that will yield a margin of error within 1.9 of
the population mean is:
Chapter 8
36. A researcher wants to estimate the mean age of all Business Week readers at a 99%
confidence level. She wants the margin of error to be within 3.1 years of the population
mean. The standard deviation of ages of all Business Week readers is 10.04 years. The
sample size that will yield a margin of error within 3.1 of the population mean is:
37. A company wants to estimate the mean net weight of all 32-ounce packages of its
Yummy Taste cookies at a 95% confidence level. The margin of error is to be within
0.025 ounces of the population mean. The population standard deviation is 0.096 ounces.
The sample size that will yield a margin of error within 0.025 ounces of the population
mean is:
38. A researcher wants to make a 99% confidence interval for a population proportion. A
preliminary sample produced the sample proportion of 0.680. The sample size that would
limit the margin of error to be within 0.024 of the population proportion is:
39. A researcher wants to make a 99% confidence interval for a population proportion. The
most conservative estimate of the sample size that would limit the margin of error to be
within 0.033 of the population proportion is:
40. A company wants to estimate, at a 95% confidence level, the proportion of all families
who own its product. A preliminary sample showed that 30.0% of the families in this
sample own this company’s product. The sample size that would limit the margin of
error to be within 0.045 of the population proportion is:
41. A company wants to estimate, at a 95% confidence level, the proportion of all families
who own its product. The most conservative estimate of the sample size that would limit
the margin of error to be within 0.046 of the population proportion is:
Chapter 8
42. The Labor Bureau wants to estimate, at a 90% confidence level, the proportion of all
households that receive welfare. The most conservative estimate of the sample size that
would limit the margin of error to be within 0.030 of the population proportion is:
43. The Labor Bureau wants to estimate, at a 90% confidence level, the proportion of all
households that receive welfare. A preliminary sample showed that 18.5% of households
in this sample receive welfare. The sample size that would limit the margin of error to be
within 0.036 of the population proportion is:
44. Which of the following is not part of the procedure for estimating the value of a
population parameter?
A) Selecting a sample
B) Collecting the required information from the members of the sample
C) Calculating the value of the sample statistic
D) Calculating the exact value of the corresponding population parameter
45. You are estimating the mean waiting time in line at a particular fast-food restaurant. You
ask 30 customers, at varying times of the day, how long they waited in line before placing
their order. You then take the average of these values and use this average to estimate the
mean waiting time for all customers. The average of the 30 values is an example of a(n):
A) Chebyshev estimate C) interval estimate
B) point estimate D) confidence estimate
46. A scientist is estimating the mean lifetime of a newly-discovered insect. From a sample
of 88 insects, she finds a sample mean of 49.2 days. Suppose that the population standard
deviation of all lifetimes is 2.500 days. What are the boundaries for a 90% confidence
interval for the mean lifetime of the insect, rounded to two decimal places?
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47. The Eks Survey Company employs 2000 people to conduct telephone surveys. Because
many people don’t like to answer such surveys, many “hang-ups” (whereby the person
hangs up without completing the survey) occur. The owner of Eks wants to determine the
mean number of “hang-ups” per employee on a particular day, using 95% confidence. He
samples 50 employees, and finds that the mean number of “hang-ups” on that day was
41.0. Suppose that the standard deviation of the number of “hang-ups” for all employees
is 21.8 What is the value of the margin of error? (round to four decimal places)
48. We are using the mean of a sample as a point estimate for the mean of a normal
distribution with a standard deviation of 5. The margin of error, with 95% confidence, for
this estimate is 0.860. What is the sample size?
49. A t distribution has a standard deviation of
1
3
n
n
−
−
. If the standard deviation is equal to
1.1055, what is the value of the t critical value for a 90% confidence interval?
50. Which of the following is not an acceptable condition for using the t distribution to make
a confidence interval for
?
A) The population from which the sample is drawn is right-skewed
B) The population from which the sample is drawn is normal
C) The population standard deviation is unknown
D) The population distribution has a mean of zero
51. Each employee of a large company is encouraged to contribute, through payroll
deduction, to an international charity. Annual contributions per employee follow
(approximately) a normal distribution. You take a random sample of 25 employees and
find that the sample mean annual contribution per employee is $501 with a standard
deviation of $17.00. What are the boundaries for a 99% confidence interval for the
population mean, rounded to two decimal places?
Chapter 8
52. In a 1997 poll of 261 male, married, upper-level managers conducted by Joy Schneer and
Frieda Reitman for Fortune magazine, 31% of the men stated that their wives worked
either full-time or part-time (Fortune, March 17, 1997). What are the boundaries for a
99% confidence interval for p, the proportion of all male, married, upper-level managers
whose wives work?
53. An advisor to the mayor of a large city wants to estimate, within 2.450 minutes, the mean
travel time to work for all employees who work within the city limits. He knows that the
standard deviation of all travel times is 11.35 minutes. He also wants to achieve a 95%
confidence interval. He will poll a random sample of city employees. How many
employees should he poll?
54. Determine the sample size n that is required for estimating the population mean. The
population standard deviation
and the desired margin of error are specified.
150
=
94% margin of error 3
A) 8,836 B) 8,836 C) 8,835 D) 8,837
55. An employee of the College Board analyzed the mathematics section of the SAT for 97
students and finds
x
= 30.2 and s = 13.0. She reports that a 97% confidence interval for
the mean number of correct answers is (27.336, 33.064). Does the interval (27.336,
33.064) cover the true mean?
Which of the following alternatives is the best answer for the above question?
A) Yes, (27.336, 33.064) covers the true mean.
B) No, (27.336, 33.064) does not cover the true mean.
C) We will never know whether (27.336, 33.064) covers the true mean.
D) The true mean will never be in (27.336, 33.064).
Chapter 8
56. Out of a sample of 639 gasoline purchases at a self-service gas station, 544 were made
with a credit or debit card. Obtain the predeterminated margin of error. Round your
answer to three decimal places.
57. In a random sample of 53 items produced by a machine, the quality control staff found 5
of them to be defective. Calculate the point estimate of the population proportion of
defective items. Round to 4 decimal places.
58. A random sample of 354 persons showed that 306 do not have health insurance.
Calculate the point estimate of the population proportion of persons who do not have
health insurance. Round to 4 decimal places.
59. The correct formula for the limits of a confidence interval is:
A)
( )
z, zxx−+
B)
( )
margin of error, margin of errorzz−+
C)
( )
margin of error, margin of errorxx−+
D)
( )
–margin of error, margin of errorxx
60. True or False. The statement: “The 90% confidence interval for the mean is (29.83 ,
50.1).” can be interpreted to mean that the probability that the mean lies in the range
(29.83 , 50.1) is 90%.