COMM 291
Application of Statistics in Business (fall 2015)
ASSIGNMENT 5
Hard Copy Solutions to be Handed In
2:30 pm, Wednesday November 18, 2015
Instructions:
This assignment consists of 10 questions/problems. Answer/solve the questions/problems in the same
order they are asked.
Use the posted cover page. This is mandatory. Assignments without properly completed cover pages
will be penalised by reducing one mark.
When formatting numbers in Excel, display only as many decimal places as provide decision-making
value to the reader. Similarly, any computations made by hand should be rounded to as many decimal
places (and no more) as required by the reader to make an informed decision. Maintain all precision in
your calculations when performing multi-step computations and round only final reported figures.
Problem 1 (4 points)
Schadek Silkscreen Printing Inc. purchases plastic cups on which to print logos for sporting events,
proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large shipment this
morning. To ensure the quality of the shipment, he selected a random sample of 300 cups. He found 15 to
be defective.
a. What is the estimated proportion that was defective in the population? (1 point)
b. Develop a 95% confidence interval for the proportion that was defective. (2 points)
c. Zack has an agreement with his supplier that he is to return lots that are 10% or more defective.
Should he return this lot? Explain your decision. (1 point)
Problem 2 (4 points)
Suppose that the prime minister wants an estimate of the proportion of the population that supports his
current policy on health care. The prime minister wants the estimate to be within 0.04 of the true
proportion. Assume a 95% level of confidence. The prime minister’s political advisors estimated the
proportion supporting the current policy to be 0.60.
a. How large a sample is required? (2 points)
b. How large a sample would be necessary if no estimate were available for the proportion that
supports current policy? (2 points)
Problem 3 (4 points)
The manager of Apache Burger felt that an average of 70 customers made purchases daily between the
hours of 3 p.m. and 5 p.m. A random sample over 50 days showed the sample mean to be 68.6 customers
with a standard deviation of 8.2 hours.
a. Using the sample data, construct a 99% confidence interval for the population mean. (2 points)
b. Does the 99% confidence interval include the value suggested by the manager? Interpret this
result. (1 point)
c. Suppose you decided to switch from a 99% confidence interval to a 95% confidence interval.
Without performing any calculations, will the interval increase, decrease, or stay the same?
Which of the values in the formula will change? (1 point)
Problem 4 (4 points)
The Simcoe County Food Emporium claims that “the typical customer spends $60 per visit.” A sample of
12 customers revealed the following purchases, in dollars, spent last visit:
64
66
64
66
59
62
67
61
64
58
54
66
a. What is the point estimate of the population mean and standard deviation? (1 point)
b. Develop a 90% confidence interval for the population mean. (2 points)
c. Is the restaurant’s claim that the “typical customer” spends $60 per visit reasonable? Justify your
answer. (1 point)
Problem 5 (6 points)
The National Bank, like most other large banks, found that using automatic teller machines (ATMs)
reduces the cost of routine bank transactions. National installed an ATM in the corporate offices of the
Fun Toy Company. The ATM is for the exclusive use of Fun’s 605 employees. After several months of
operation, a sample of 100 employees revealed the following use of the ATM machine by Fun employees
in a month:
# of time ATM used
0
1
2
3
4
5
Frequency
25
30
20
10
10
5
a. What is the estimate of the proportion of employees who do not use the ATM in a month? (1
point)
b. Develop a 95% confidence interval for this estimate. Can National be sure that at least 40% of the
employees of Fun Toy Company will use the ATM? (2 points)
c. How many transactions does the average Fun employee make per month? (1 point)
d. Develop a 95% confidence interval for the mean number of transactions per month. (1 point)
e. Is it possible that the population mean is 0? Explain. (1 point)
Problem 6 (3 points)
A research organization surveyed 1016 Canadian adults (assume 50/50 split between men and women)
and found that 65% of men and 45% of women support scrapping the penny.
a. Construct a 90% confidence interval for the difference in support for scrapping the penny
between men and women. (1 point)
b. Construct a 99% confidence interval for the difference in support for scrapping the penny
between men and women. (1 point)
c. Interpret the meaning of the fact that one of these confidence intervals is wider than the others. (1
point)
Problem 7 (5 points)
The owner of Britten’s Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample
of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs per
month.
a. What is the value of the population mean? What is the best estimate of this value? (1 point)
b. Explain why we need to use the t distribution. What assumption do you need to make? (1 point)
c. For a 95% confidence interval, what is the value of t? (1 point)
d. Develop the 95% confidence interval for the population mean. (1 point)
e. Would it be reasonable to conclude that the population mean is 21 eggs? What about 25 eggs? (1
point)
Problem 8 (5 points)
Dr. Susan Benner is an industrial psychologist. She is currently studying stress among executives of
Internet companies. She has developed a questionnaire that she believes measures stress. A score above
80 indicates stress at a dangerous level. A random sample of 15 executives revealed the following stress
level scores:
94
78
83
90
78
99
97
90
97
90
93
94
100
75
84
a. Find the mean stress level for this sample. What is the point estimate of the population mean? (1
point)
b. Construct a 95% confidence level for the population mean. (1 point)
c. Is it reasonable to conclude that Internet executives have a mean stress level in the dangerous
level, according to Dr. Benner’s test? (1 point)
Problem 9 (6 points)
The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be
driven before the tread wears out is 96 600 km. The population standard deviation of the mileage is 8050
km. The Crosset Truck Company bought 48 tires and found that the mean mileage for its trucks is 95 795
km. Is Crosset’s experience different from that claimed by the manufacturer at the 0.05 level of
significance.
a.
b.
c.
d.
e.
What are the hypotheses? Is this a one- or two-tailed test? (1 point)
What is the decision rule? (1 point)
What is the value of the test statistic? (1 point)
What is your decision regarding H0? (1 point)
Determine the p-value and interpret it. (2 points)
Problem 10 (4 points)
During the recent seasons, Major League Baseball has been criticized for the length of games. A report
indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the
following times to completion. (Note that the minutes have been changed to fractions of hours, so that a
game that lasted 2 hours and 24 minutes is reported at 2.40 hours.)
Can we conclude that the mean time for a game is less than 3.50 hours? Use the 0.05 significance level.
