Chapter 3:
3-1. A random sample of 15 articles in Fortune
revealed the
following word counts per article:
5,176 6,005 5,052 5,310 4,188
4,132 5,736 5,381 4,983 4,423
5,002 4,573 4,209 5,611 4,568
Compute the mean, median, first quartile, and
third
quartile for these sample data
55 46 58 67 66 73 81 48 59 70
a. Determine the median scores for the
statistics test.
b. Determine the 25th and 75th percentiles for
the
statistics test scores.
c. Determine the 60th percentile for the
statistics test
scores
3-5. A random sample of the miles driven by 20
rental car
customers is shown as follows:
90 85 100 150
125 75 50 100
75 60 35 90
100 125 75 85
50 100 50 80
Develop a box and whisker plot for the sample
data.
3-9. A food manufacturer recently found that
there is a
huge variation in the weight of chickens
supplied by a
local farm. To justify their suspicion, the
manufacturer
randomly selects 20 chickens and notes the
weight of
each (in kg) as follows:
0.95 1.09 0.88 1.1 0.9 1 0.93 1.13 1.09 1.05
1.1 0.99 1.03 1.03 0.86 0.94 0.98 0.97 1.09 0.95
a. Compute the mean, median, and mode for
the
chickens’ weights.
b. Interpret your findings in part a.
c. Construct a box and whisker plot for the
chickens’
weights and determine the distribution’s shape
for
the chickens’ weights, which will help justify the
manufacturer’s suspicion.
3-6. Examine the following data:
23 65 45 19 35 28 39 100 50 26 25 27
24 17 12 106 23 19 39 70 20 18 44 31
a. Compute the quartiles.
b. Calculate the 90th percentile.
c. Develop a box and whisker plot.
d. Calculate the 20th and the 30th percentiles.
3-7. Consider the following scores for a statistics
test that has
been selected from students who attend Bright
University:
65 82 73 91 95 86 78 69 80 88
3-25. Google is noted for its generous employee
benefits.
The following data reflect the number of
vacation days
that a sample of employees at Google have left
to take
before the end of the year:
30201352
51300133
43184240
a. Compute the range for these sample data.
b. Compute the variance for these sample data.
3-4. The ages of 15 employees selected from a
company are
as follows:
53 32 61 27 39
44 45 57 25 28
33 35 36 33 41
Calculate the mean, median, first quartile, and
third
quartiles for the sample employees’ ages.
c. Compute the standard deviation for these
sample data.
3-27. The following data are the population of
ages of students
who have recently purchased a sports video
game:
16 15 17 15 15 15
14 9 16 15 13 10
8 18 20 17 17 17
18 23 7 15 20 10
14 14 12 12 24 21
a. Compute the population variance.
b. Compute the population standard deviation.
3-29. The following data show the number of
hours spent
watching television for 12 randomly selected
freshmen
attending a liberal arts college in the Midwest:
Hours of Television Viewed Weekly
7.5 11.5 14.4 7.8
13.0 10.3 5.4 12.0
12.2 8.9 8.5 6.6
Calculate the range, variance, standard
deviation, and interquartile range for the
sample data.
3-30. Consider the following two separate
samples:
27 27 25 12 15 10 20 37 31 35
and
1 3 2 16 18 16 16 4 16 118
a. Calculate the range, variance, standard
deviation, and interquartile range for each data
set.
b. Which data set is more spread out based on
these
statistics?
c. Now remove the largest number from each
data set and repeat the calculations called for in
part a.
d. Compare the results of parts a and c. Which
statistic
seems to be more affected by outliers?
3-33. A random sample of 20 pledges to a public
radio fundraiser revealed the following dollar
pledges:
90 85 100 150
125 75 50 100
75 60 35 90
100 125 75 85
50 100 50 80
a. Compute the range, variance, standard
deviation,
and interquartile range for these sample data.
b. Briefly explain the difference between the
range
and the interquartile range as a measure of
dispersion
3-35. A college registrar has been asked to
prepare a report
about the graduate students. Among other
things, she
wants to analyze the ages of the students. She
has
taken a sample of ten graduate students and
has found
the following ages:
32 22 24 27 27 33 28 23 24 21
a. Compute the range, interquartile range, and
standard deviation for these data.
b. It is thought that the mean age of graduate
students
in U.S. colleges and universities is 37.8 years.
Based on your calculations in part a, what might
you conclude about the age of students in this
college’s programs?
3-39. Employers typically provide Internet
access to assist
employees in work-related activities. An IT
department
officer is monitoring the Internet data usage in
a company. She collects the daily amount of
data usage
(in GB) for a period of 20 days:
45 48 47 46 39
41 35 33 48 44
38 42 44 50 44
40 36 45 49 45
a. Calculate the range, interquartile range, and
standard deviation for these data.
b. Which of the finding in part a best represents
the variation of daily amount of data usage for
the
company? Explain.
c. What does the standard deviation indicate
about the company’s daily amount of data
usage.
3-51. Two distributions of data are being
analyzed.
Distribution A has a mean of 500 and a standard
deviation equal to 100. Distribution B has a
mean of 10
and a standard deviation equal to 4.0. Based on
this information, use the coefficient of variation
to
determine which distribution has greater
relative variation.
3-54. The following data represent random
samples taken
from two different populations, A and B:
A 31 10 69 25 62 61 46 74 57
B 1,030 1,111 1,155 978 943 983 932 1,067
1,013
a. Compute the mean and standard deviation
for the
sample data randomly selected from Population
A.
b. Compute the mean and standard deviation
for the
sample data randomly selected from Population
B.
c. Which sample has the greater spread when
measured by the standard deviation?
d. Compute the coefficient of variation for the
sample
data selected from Population A and from
Population B. Which sample exhibits the greater
relative variation?
3-61. Thirty people were given an employment
screening
test, which is supposed to produce scores that
are
distributed according to a bell-shaped
distribution. The
following data reflect the scores of those 30
people:
76 75 74 56 61 76
62 96 68 62 78 76
84 67 60 96 77 59
67 81 66 71 69 65
58 77 82 75 76 67
The employment agency has in the past issued
a rejection letter with no interview to the lower
16%
taking the test. They also send the upper 2.5%
directly
to the company without an interview. Everyone
else is interviewed. Based on the data and the
assumption of a
bell-shaped distribution, what scores should be
used
for the two cutoffs?
Chapter 5:
5-1. An economics quiz contains six multiplechoice
questions. Let x represent the number of
questions a
student answers correctly.
a. Is x a continuous or discrete random
variable?
b. What are the possible values of x?
5-3. If the Prudential Insurance Company
surveys its
customers to determine the number of children
under
age 22 living in each household,
a. What is the random variable for this survey?
b. Is the random variable discrete or
continuous?
5-4. Given the following discrete probability
distribution:
x
P(x)
50
0.375
65
0.15
70
0.225
75
0.05
90
0.20
a. Calculate the expected value of x.
b. Calculate the variance of x.
c. Calculate the standard deviation of x.
5-5. Because of weather issues, the number of
days next
week that the captain of a charter fishing boat
can leave
port is uncertain. Let x = number of days the
boat is
able to leave port per week. The following
probability
distribution for the variable, x, was determined
based
on historical data when the weather was poor:
x
P(x)
0
0.05
1
0.10
2
0.10
3
0.20
4
0.20
5
0.15
6
0.15
7
0.05
Based on the probability distribution, what is
the expected number of days per week the
captain can leave port?
5-13. Before a book is sent for printing, Anna, a
proofreader,
needs to ensure that there are no grammatical
or typographical errors in any page. Based on
her past experiences, she found the probability
for the number of errors per page in a book
shown as follows:
Number of Errors Probability
2
0.19
3
0.31
4
0.23
5
0.14
6
0.13
a. What is the probability that a book has 4 or
more
errors in a page?
b. Compute the average number of errors per
page in a book.
c. Calculate the standard deviation for errors
per page in a book and interpret it.
5-22. Suppose that 20% of credit cards have an
outstanding
balance at the credit card limit. A bank manager
randomly selects 15 customers and finds 4 that
have balances at the limit. Assume that the
properties of the binomial distribution apply.
a. What is the probability of finding 4 customers
in a sample of 15 who have “maxed out” their
credit cards?
b. What is the probability that 4 or fewer
customers in the sample will have balances at
the limit of the credit card?
5-25. If a binomial distribution applies with a
sample size of
n = 20, find
a. the probability of 5 successes if the
probability of a
success is 0.40
b. the probability of at least 7 successes if the
probability of a success is 0.25
c. the expected value, n = 20, p = 0.20
d. the standard deviation, n = 20, p = 0.20
5-28. Assuming the binomial distribution applies
with a sample size of n = 15, find
a. the probability of 5 or more successes if the
probability of a success is 0.30
b. the probability of fewer than 4 successes if
the probability of a success is 0.75
c. the expected value of the random variable if
the
probability of success is 0.40
d. the standard deviation of the random
variable if the
probability of success is 0.40
5-29. A random variable follows a binomial
distribution with
a probability of success equal to 0.65. For a
sample
size of n = 7, find
a. the probability of exactly 3 successes
b. the probability of 4 or more successes
c. the probability of exactly 7 successes
d. the expected value of the random variable
5-33. Given a binomial distribution with n = 8
and p = 0.40, obtain the following:
a. the mean
b. the standard deviation
c. the probability that the number of successes
is larger
than the mean
d. the probability that the number of successes
is within {2 standard deviations of the mean
5-41. A small hotel in a popular resort area has
20 rooms.
The hotel manager estimates that 15% of all
confirmed
reservations are “no-shows.” Consequently, the
hotel accepts confirmed reservations for as
many as 25 rooms. If more confirmed
reservations arrive than there
are rooms, the overbooked guests are sent to
another hotel and given a complimentary
dinner. If the hotel currently has 25 confirmed
reservations, find
a. the probability that no customers will be sent
to
another hotel
b. the probability that exactly 2 guests will be
sent to
another hotel
c. the probability that 3 or more guests will be
sent to
another hotel?
5-43. The Employee Benefit Research Institute
reports that
58% of workers say they are confident they
have saved
enough for retirement (source: “The 2015
Retirement
Confidence Survey: Having a retirement savings
plan a key factor in Americans’ retirement
confidence, EBRI Issue Brief #413, April 2015).
a. If a random sample of 30 workers is taken,
what is
the probability that fewer than 17 workers are
confident?
5-51. Arrivals to a bank automated teller
machine (ATM) are
distributed according to a Poisson distribution
with a mean equal to three per 15 minutes.
a. Determine the probability that in a given 15minute
segment, no customers will arrive at the ATM.
b. What is the probability that fewer than four
customers will arrive in a 30-minute segment?
5-53. A population of 10 items contains 3 that
are red and 7
that are green. What is the probability that in a
random sample of 3 items selected without
replacement, 2 red
and 1 green items are selected?
5-64. John Thurgood founded a company that
translates
Chinese books into English. His company is
currently
testing a computer-based translation service.
Since
Chinese symbols are difficult to translate, John
assumes the computer program will make some
errors,
but then so do human translators. The
computer error
rate is supposed to be an average of 3 per 400
words of translation. Suppose John randomly
selects a 1,200- word passage. Assuming that
the Poisson distribution applies and that the
computer error rate is actually 3
errors per 400 words,
a. determine the probability that no errors will
be
found
b. calculate the probability that more than 14
errors
will be found
c. find the probability that fewer than 9 errors
will be
found
d. If 15 errors are found in the 1,200-word
passage,
what would you conclude about the computer
company’s claim? Why?
5-73. How is the shape of the binomial
distribution changed for a given value of p as
the sample size is increased? Discuss.
5-76. Consider an experiment in which a sample
of size
n = 5 is taken from a binomial distribution.
a. Calculate the probability of each value of the
random
variable for the probability of a success equal to
(1) 0.1, (2) 0.25, (3) 0.50, (4) 0.75, and (5) 0.9.
b. Which probabilities produced a right-skewed
distribution? Why?
c. Which probability of a success yielded a
symmetric
distribution? Why?
d. Which probabilities produced a left-skewed
distribution? Discuss why.
Chapter 6:
6-1. For a normally distributed population with
m = 200
and s = 20, determine the standardized z-value
for each of the following:
a. x = 225
b. x = 190
c. x = 240
6-3. For a standardized normal distribution,
calculate the
following probabilities:
a. P10.00 6 z … 2.332
b. P1-1.00 6 z … 1.002
c. P11.78 6 z 6 2.342
6-4. For a standardized normal distribution,
determine a
value, say z0, so that
a. P10 6 z 6 z02 = 0.4772
b. P1-z0 … z 6 02 = 0.45
c. P1-z0 … z … z02 = 0.95
d. P1z 7 z02 = 0.025
e. P1z … z02 = 0.01
6-5. Consider a random variable, z, that has a
standardized
normal distribution. Determine the following
probabilities:
a. P10 6 z 6 1.962
b. P1z 7 1.6452
c. P11.28 6 z … 2.332
d. P1-2 … z … 32
e. P1z 7 -12
6-7. For the following normal distributions with
parameters
as specified, calculate the required
probabilities:
a. m = 5, s = 2; calculate P10 6 x 6 82.
b. m = 5, s = 4; calculate P10 6 x 6 82.
c. m = 3, s = 2; calculate P10 6 x 6 82.
d. m = 4, s = 3; calculate P1x 7 12.
e. m = 0, s = 3; calculate P1x 7 12
6-8. A population is normally distributed with m
= 100
and s = 20.
a. Find the probability that a value randomly
selected
from this population will be greater than 130.
b. Find the probability that a value randomly
selected
from this population will be less than 90.
c. Find the probability that a value randomly
selected
from this population will be between 90 and
130.
6-9. A random variable is known to be normally
distributed
with the following parameters:
m = 5.5 and s = 0.50
a. Determine the value of x such that the
probability of
a value from this distribution exceeding x is at
most
0.10.
b. Referring to your answer in part a, what must
the
population mean be changed to if the
probability of exceeding the value of x found in
part a is reduced from 0.10 to 0.05?
6-11. Assume that a random variable is
normally distributed
with a mean of 1,500 and a variance of 324.
a. What is the probability that a randomly
selected
value will be greater than 1,550?
b. What is the probability that a randomly
selected
value will be less than 1,485?
c. What is the probability that a randomly
selected
value will be either less than 1,475 or greater
than
1,535?
6-15. Doggie Nuggets Inc. (DNI) sells large bags
of dog
food to warehouse clubs. DNI uses an
automatic filling
process to fill the bags. Weights of the filled
bags are approximately normally distributed
with a mean of 50 kilograms and a standard
deviation of 1.25 kilograms.
a. What is the probability that a filled bag will
weigh
less than 49.5 kilograms?
b. What is the probability that a randomly
sampled
filled bag will weigh between 48.5 and 51
kilograms?
c. What is the minimum weight a bag of dog
food could
be and remain in the top 15% of all bags filled?
d. DNI is unable to adjust the mean of the filling
process. However, it is able to adjust the
standard
deviation of the filling process. What would the
standard deviation need to be so that no more
than 2% of all filled bags weigh more than 52
kilograms?
6-17. The average number of acres burned by
forest and
range fires in a large county in the West is 5,300
acres per year, with a standard deviation of 750
acres. The distribution of the number of acres
burned is normal.
a. Compute the probability that more than
6,000 acres
will be burned in any year.
b. Determine the probability that fewer than
5,000
acres will be burned in any year.
c. What is the probability that between 3,500
and
5,200 acres will be burned?
d. In those years when more than 6,500 acres
are burned, help is needed from eastern-region
fire
teams. Determine the probability help will be
needed in any year
6-23. A maternity wear designer sells dresses
and pants
priced around $150 each for an average total
sale of
$1,200. The total sale has a normal distribution
with a
standard deviation of $350.
a. Calculate the probability that a randomly
selected
customer will have a total sale of more than
$1,500.
b. Compute the probability that the total sale
will be
within {2 standard deviations of the mean total
sales.
c. Determine the median total sale
6-52. Recall the Empirical Rule from Chapter 3.
It states that
if the data distribution is bell-shaped, then the
interval
m { s contains approximately 68% of the values,
m { 2s contains approximately 95%, and m { 3s
contains virtually all of the data values. The bellshaped
distribution referenced is the normal
distribution.
a. Verify that a standard normal distribution
contains
approximately 68% of the values in the interval
m
b. Verify that a standard normal distribution
contains
approximately 95% of the values in the interval
m
c. Verify that a standard normal distribution
contains
virtually all of the data in the interval m { 3s
6-61. Two automatic dispensing machines are
being
considered for use in a fast-food chain. The first
dispenses an amount of liquid that has a normal
distribution with a mean of 11.9 ounces and a
standard
deviation of 0.07 ounce. The second dispenses
an amount of liquid that has a normal
distribution with a
mean of 12.0 ounces and a standard deviation
of 0.05 ounce. Acceptable amounts of
dispensed liquid are between 11.9 and 12.0
ounces. Calculate the relevant
probabilities and determine which machine
should be
selected
6-67. A traffic control camera at a busy
intersection records,
on average, 5 traffic violations per hour.
Assume that the random variable number of
recorded traffic violations
follows a Poisson distribution.
a. What is the probability that the next
recorded
violation will occur within 5 minutes?
b. How likely is it that no traffic violations will
be recorded within the next 7 minutes?
6-71. Assume that the amount of time eighthgraders take to
complete an assessment examination is 78
minutes with
a standard deviation of 12 minutes.
a. What proportion of eighth-graders complete
the
assessment examination in 72 minutes or less?
b. What proportion of eighth-graders complete
the
assessment examination in 82 minutes or
more?
c. For what number of minutes would 90% of all
eighth-graders complete the assessment
examination?
Chapter 7:
7-1. A population has a mean of 125. If a
random sample of
8 items from the population results in the
following
sampled values, what is the sampling error for
the
sample?
103 123 99 107 121 100 100 99
7-2. The following data are the 16 values in a
population:
10 5 19 20 10 8 10 2
14 18 7 8 14 2 3 10
a. Compute the population mean.
b. Suppose a simple random sample of 5 values
from
the population is selected with the following
results:
5 10 20 2 3
Compute the mean of this sample.
c. Based on the results for parts a and b,
compute the
sampling error for the sample mean.
7-3. The following population is provided:
17 15 8 12 9 7 9 11
12 14 16 9 5 10 14 13
12 12 11 9 14 8 14 12
Further, a simple random sample from this
population
gives the following values:
12 9 5 10 14 11
Compute the sampling error for the sample
mean in this situation.
7-5. Assume that the following represent a
population of
N = 24 values:
10 14 32 9 34 19 31 24
33 11 14 30 6 27 33 32
28 30 10 31 19 13 6 35
a. If a random sample of n = 10 items includes
the
following values, compute the sampling error
for
the sample mean:
32 19 6 11 10
19 28 9 13 33
b. For a sample of size n = 6, compute the range
for
the possible sampling error. (Hint: Find the
sampling
error for the 6 smallest sample values and the
6 largest sample values.)
7-10. An Internet service provider states that
the average
number of hours its customers are online each
day is
3.75. Suppose a random sample of 14 of the
company’s
customers is selected and the average number
of hours
that they are online each day is measured. The
sample
results are
3.11 1.97 3.52 4.56 7.19 3.89 7.71
2.12 4.68 6.78 5.02 4.28 3.23 1.29
Based on the sample of 14 customers, how
much
sampling error exists? Would you expect the
sampling error to increase or decrease if the
sample size was increased to 40?
7-15. A computer lab at a small college has 25
computers. Twice
during the day, a full scan for viruses is
performed on each
computer. Because of differences in the
configuration of
the computers, the times required to complete
the scan are
different for each machine. Records for the
scans are kept
and indicate that the time (in seconds) required
to perform
the scan for each machine is as shown here.
Time in Seconds to Complete Scan
1,500 1,347 1,552 1,453 1,371
1,362 1,447 1,362 1,216 1,378
1,647 1,093 1,350 1,834 1,480
1,522 1,410 1,446 1,291 1,601
1,365 1,575 1,134 1,532 1,534
a. What is the mean time required to scan all
25 computers?
b. Suppose a random sample of 5 computers is
taken and
the scan times for each are as follows: 1,534,
1,447,
1,371, 1,410, and 1,834. If these 5 randomly
sampled
computers are used to estimate the mean scan
time for
all 25 computers, what would the sampling
error be?
c. What is the range of possible sampling error
if a random sample size of 7 computers is taken
to estimate the mean scan time for all 25
machines?
7-22. A population with a mean of 1,250 and a
standard
deviation of 400 is known to be highly skewed
to the right. If a random sample of 64 items is
selected from
the population, what is the probability that the
sample
mean will be less than 1,325?
7-23. Suppose that a population is known to be
normally
distributed with m = 2,000 and s = 230. If a
random sample of size n = 8 is selected,
calculate the
probability that the sample mean will exceed
2,100.
7-24. A normally distributed population has a
mean of 500
and a standard deviation of 60.
a. Determine the probability that a random
sample of
size 16 selected from this population will have a
sample mean less than 475.
b. Determine the probability that a random
sample of
size 25 selected from the population will have a
sample mean greater than or equal to 515.
7-33. Suppose the life of a particular brand of
calculator
battery is approximately normally distributed
with a mean of 75 hours and a standard
deviation of 10 hours.
a. What is the probability that a single battery
randomly selected from the population will
have a life between 70 and 80 hours?
b. What is the probability that 16 randomly
sampled batteries from the population will have
a sample
mean life of between 70 and 80 hours?
c. If the manufacturer of the battery is able to
reduce
the standard deviation of battery life from 10 to
9 hours, what would be the probability that
16 batteries randomly sampled from the
population will have a sample mean life of
between 70 and
80 hours?
7-45. A population has a proportion equal to
0.30. Calculate
the following probabilities with n = 100:
a. P1p … 0.352
b. P1p 7 0.402
c. P10.25 6 p … 0.402
d. P1p Ú 0.272.
7-46. If a random sample of 200 items is taken
from a
population in which the proportion of items
having a
desired attribute is p = 0.30, what is the
probability
that the proportion of successes in the sample
will be
less than or equal to 0.27?
7-49. Given a population in which the
probability of success
is p = 0.20, if a sample of 500 items is taken,
then
a. Calculate the probability the proportion of
successes
in the sample will be between 0.18 and 0.23.
b. Calculate the probability the proportion of
successes
in the sample will be between 0.18 and 0.23 if
the
sample size is 200.
7-57. Ten percent of engineers (electrical,
mechanical, civil,
and industrial) are women (source: Rebecca
Adams,
“40 Percent of female engineers are leaving the
field.
This might be why,” www.huffingtonpost.com,
Aug. 12, 2014). Suppose a random sample of 50
engineers is selected.
a. How likely is it that the random sample of 50
engineers
will contain 8 or more women in these
positions?
b. How likely is it that the random sample will
contain
fewer than 5 women in these positions?
c. If the random sample included 200 engineers,
how
would this change your answer to part b?
Chapter 8:
8-1. Assuming the population of interest is
approximately
normally distributed, construct a 95%
confidence interval estimate for the population
mean given the following values:
x = 18.4 s = 4.2 n = 13
8-2. Construct a 90% confidence interval
estimate for the population mean given the
following values:
x = 70 s = 15 n = 65
8-4. Construct a 98% confidence interval
estimate for the
population mean given the following values:
x = 120 s = 20 n = 50
8-6. Determine the margin of error for a
confidence interval
estimate for the population mean of a normal
distribution given the following information:
a. confidence level = 0.98, n = 13, s = 15.68
b. confidence level = 0.99, n = 25, s = 3.47
c. confidence level = 0.98, standard error =
2.356
8-7. The following sample data have been
collected based
on a simple random sample from a normally
distributed population:
28023
53142
a. Compute a 90% confidence interval estimate
for the
population mean.
b. Show what the impact would be if the
confidence
level is increased to 95%. Discuss why this
occurs.
8-8. A random sample of size 20 yields x = 3.13
and
s2 = 1.45. Calculate a confidence interval for the
population mean whose confidence level is as
follows:
a. 0.99
b. 0.98
c. 0.95
d. 0.90
e. 0.80
f. What assumptions were necessary to
establish the
validity of the confidence intervals calculated in
parts a through e?
8-9. A random sample of n = 12 values taken
from a
normally distributed population resulted in the
following sample values:
107 109 99 91 103 105
105 94 107 94 97 113
Use the sample information to construct a 95%
confidence interval estimate for the population
mean.
8-10. A random sample of n = 9 values taken
from a
normally distributed population with a
population
variance of 25 resulted in the following sample
values:
53 46 55 45 44 52 46 60 49
Use the sample values to construct a 90%
confidence
interval estimate for the population mean.
8-11. A random sample was selected from a
population
having a normal distribution. Calculate a 90%
confidence interval estimate for m for each of
the
following situations:
a. Σx = 134, n = 10, s = 3.1
b. Σx = 3,744, n = 120, s = 8.2
c. Σx = 40.5, n = 9, s = 2.9
d. Σx = 585.9, Σx2 = 15,472.37, n = 27
(Hint: Refer to Equation 3.13.)
8-12. Allante Pizza delivers pizzas throughout its
local
market area at no charge to the customer.
However,
customers often tip the driver. The owner is
interested
in estimating the mean tip income per delivery.
To do
this, she has selected a simple random sample
of
12 deliveries and has recorded the tips that the
drivers
received. These data are
$2.25 $2.50 $2.25 $2.00 $2.00 $1.50
$0.00 $2.00 $1.50 $2.00 $3.00 $1.50
a. Based on these sample data, what is the best
point
estimate to use as an estimate of the true mean
tip
per delivery?
b. Suppose the owner is interested in
developing a 90% confidence interval estimate.
Given the fact that the
population standard deviation is unknown,
what
distribution will be used to obtain the critical
value?
c. Referring to part b, what assumption is
required to
use the specified distribution to obtain the
critical
value? Develop a box and whisker plot to
illustrate
whether this assumption seems to be
reasonably
satisfied.
d. Referring to parts b and c, construct and
interpret
the 90% confidence interval estimate for the
population mean.
8-13. The BelSante Company operates retail
pharmacies
in 10 eastern states. The company’s internal
audit
department selected a random sample of 300
prescriptions issued throughout the system. The
objective of the sampling was to estimate the
average
dollar value of all prescriptions issued by the
company.
The following data were collected:
x = +14.23
s = 3.00
a. Determine the 90% confidence interval
estimate for
the true average sales value for prescriptions
issued
by the company. Interpret the interval estimate.
b. One of its retail outlets reported that it had
monthly
revenue of $7,392 from 528 prescriptions. Are
such
results to be expected? Do you believe that the
retail outlet should be audited? Support your
answer with
calculations and logic.
8-27. What sample size is needed to estimate a
population
mean within {50 of the true mean value using a
confidence level of 95%, if the true population
variance
is known to be 122,500?
8-28. An advertising company wishes to
estimate the mean
household income for all single working
professionals
who own a foreign automobile. If the
advertising
company wants a 90% confidence interval
estimate
with a margin of error of { +2,500, what sample
size
is needed if the population standard deviation is
known
to be $27,500?
8-30. A sample size must be determined for
estimating a
population mean given that the confidence
level is 90%
and the desired margin of error is 0.30. The
largest
value in the population is thought to be 15 and
the
smallest value is thought to be 5. Calculate the
sample
size required to estimate the population using a
generously large sample size. (Hint: Use the
range/6
option.)
8-31. Suppose a study estimated the population
mean for a
variable of interest using a 99% confidence
interval. If
the width of the estimated confidence interval
(the
difference between the upper limit and the
lower limits)
is 600 and the sample size used in estimating
the mean
is 1,000, what is the population standard
deviation?
8-32. Determine the smallest sample size
required to
estimate the population mean under the
following
specifications:
a. e = 2.4, confidence level = 80,, data between
50 and 150
b. e = 2.4, confidence level = 90,, data between
50 and 150
c. e = 1.2, confidence level = 90,, data between
50 and 150
d. e = 1.2, confidence level = 90,, data between
25 and 175
8-35. A production process that fills 12-ounce
cereal boxes
is known to have a population standard
deviation of
0.009 ounce. If a consumer protection agency
would like
to estimate the mean fill, in ounces, for 12ounce cereal
boxes with a confidence level of 92% and a
margin of
error of 0.001, what size sample must be used?
8-39. Apart from being fun, toys are an
important part of the
physical and mental development of children.
Parents
play a role in assisting their children in picking
the right toys. An industrial designer wants to
determine the average amount of time that
parents take in
selecting the right toys for their children. A
random sample of 36 parents yielded an
average time of 19.92 minutes in selecting toys,
with a sample standard deviation of 5.73
minutes. The designer requires a 95%
confidence interval estimation within 0.5
margin of error. Help the designer to calculate
how many more parents she needs in order to
conduct within the interval estimate.
8-48. Compute the 90% confidence interval
estimate for the
population proportion, p, based on a sample
size of 100
when the sample proportion, p, is equal to 0.40.
8-49. A pilot sample of 75 items was taken, and
the number
of items with the attribute of interest was
found to
be 15. How many more items must be sampled
to
construct a 99% confidence interval estimate
for p with
a 0.025 margin of error?
8-51. At issue is the proportion of people in a
particular county who do not have health care
insurance coverage. A simple random sample of
240 people was asked if they have insurance
coverage, and 66 replied that they did not have
coverage. Based on these sample data,
determine the 95% confidence interval estimate
for the population proportion.
8-57. A survey of 499 women revealed that 38%
wear flats
to work.
a. Use this sample information to develop a 99%
confidence interval for the population
proportion of women who wear flats to work.
b. Suppose we also wish to estimate the
proportion of women who wear athletic shoes
to work with a margin of error of 0.01 with 95%
confidence.
Determine the sample size required.
8-54. A random sample of 200 items reveals
that 144 of the items have the attribute of
interest.
a. What is the point estimate for the population
proportion for all items having this attribute?
b. Use the information from the random sample
to develop a 95% confidence interval estimate
for the population proportion, p, of all items
having this attribute of interest
8-55. A random sample of 40 television viewers
was asked if
they had watched the current week’s The Voice.
The following data represent their responses:
no no no yes no no no yes no yes
no no no yes no no no no yes no
yes no no no no yes no no no no
no no no no no no no no no no
a. Calculate the proportion of viewers in the
sample
who indicated they watched the current week’s
episode of The Voice.
b. Compute a 95% confidence interval for the
proportion
of viewers in the sample who indicated they
watched
the current week’s episode of The Voice.
c. Calculate the smallest sample size that would
produce a margin of error of 0.025 if the
population
proportion is well represented by the sample
proportion in part a.
8-76. Suppose a random sample of 197
accounts from a
corporate credit card database revealed a
sample average
balance of $2,325 with a standard deviation of
$144.
Use the sample information to develop a 95%
confidence interval for the true population of all
credit
card balances for this corporate credit card.