Assignment 4 Chapter 4

Course Title: Business Statistics II
Assignment #4
Statistical Inferences about Two Populations
Exercise #1
At the Hernandez Manufacturing Company, new employees are expected to attend a three-day
seminar to learn about the company. At the end of the seminar, they are tested to measure
their knowledge about the company. The traditional training method has been lecture and a
question-and-answer session Management decided to experiment with a different training
procedure, which processes new employees in two days by using DVDs and having no
question-and-answer session. If this procedure works, it could save the company thousands of
dollars over a period of several years. However, there is some concern about the effectiveness
of the two-day method, and company managers would like to know whether there is any
difference in the effectiveness of the two training methods.
To test the difference in the two methods, the managers randomly select two independent
samples,one group of 15 newly hired employees to take the three-day seminar (method A) and
a second group of 12 new employees for the two-day DVD method (method B). The
following Table shows the test scores of the two groups.
1- Use α= 0.05 to determine whether there is a significant difference in the mean scores
of the two groups. Assume that the scores for this test are normally distributed and that
the population variances are approximately equal.
2- Estimate the confidence Interval for the difference. Interpret
Exercise #2
Is there a difference in the way Chinese cultural values affect the purchasing strategies of
industrial buyers in Taiwan and mainland China?
A study by researchers at the National Chiao-Tung University in Taiwan attempted to
determine whether there is a significant difference in the purchasing strategies of industrial
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buyers between Taiwan and mainland China based on the cultural dimension labeled
“integration.” Integration is being in harmony with one’s self, family, and associates. For the
study, 46 Taiwanese buyers and 26 mainland Chinese buyers were contacted and interviewed.
Buyers were asked to respond to 35 items using a 9-point scale with possible answers ranging
from no importance (1) to extreme importance (9). The resulting statistics for the two groups
are shown in the following Table.
Use α=0.01 to determine whether there is a significant difference between buyers in Taiwan
and buyers in mainland China on integration.
Assume that integration scores are normally distributed in the population and that the
population variances are approximately equal.
Exercise #3
Consumers are asked to rate a company both before and after viewing a video on the company
twice a day for a week. The data are displayed in the following Table.
Use an alpha of 0.05 to test whether there is a significant increase in the ratings of the
company after the one-week video treatment. Assume that differences in ratings are normally
distributed in the population.
Exercise #4
A study of female entrepreneurs was conducted to determine their definition of success. The
women were offered optional choices such as happiness/self-fulfillment, sales/profit, and
achievement/challenge. The women were divided into groups according to the gross sales of
their businesses. A significantly higher proportion of female entrepreneurs in the $100,000 to
$500,000 category than in the less than $100,000 category seemed to rate sales/profit as a
definition of success.
Suppose you decide to test this result by taking a survey of your own and identify female
entrepreneurs by gross sales. You interview 100 female entrepreneurs with gross sales of less
than $100,000, and 24 of them define sales/profit as success.
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You then interview 95 female entrepreneurs with gross sales of $100,000 to $500,000, and 39
cite sales/profit as a definition of success.
Use this information to test whether there is a significant difference in the proportions of the
two groups that define success as sales/profit. Use α = 0.01.
Exercise #5
According to Runzheimer International, a family of four in Manhattan with $60,000 annual

income spends more than $22,000 a year on basic goods and services. In contrast, a family of
four in San Antonio with the same annual income spends only $15,460 on the same items.
Suppose we want to test to determine whether the variance of money spent per year on the
basics by families across the United States is greater than the variance of money spent on the
basics by families in Manhattan—that is, whether the amounts spent by families of four in
Manhattan are more homogeneous than the amounts spent by such families nationally.
Suppose a random sample of eight Manhattan families produces the figures in the following
table, which are given along with those reported from a random sample of seven families
across the United States.
Complete a hypothesis-testing procedure to determine whether the variance of values taken
from across the United States can be shown to be greater than the variance of values obtained
from families in Manhattan. Let α =0 .01. Assume the amount spent on the basics is normally
distributed in the population.
Exercise #6
Suppose a Realtor is interested in comparing the asking prices of midrange homes in Peoria, Illinois,
and Evansville, Indiana. The Realtor conducts a small telephone survey in the two cities, asking the
prices of midrange homes. A random sample of 21 listings in Peoria resulted in a sample average price
of $116,900, with a standard deviation of $2,300. A random sample of 26 listings in Evansville
resulted in a sample average price of $114,000, with a standard deviation of $1,750. The Realtor
assumes prices of midrange homes are normally distributed and the variance in prices in the two cities
is about the same.
1. What would he obtain for a 90% confidence interval for the difference in mean prices of midrange
homes between Peoria and Evansville?
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2. Test whether there is any difference in the mean prices of midrange homes of the two cities for α=
0.10.
Exercise #7
Companies that recently developed new products were asked to rate which activities are most difficult
to accomplish with new products. Options included such activities as assessing market potential,
market testing, finalizing the design, developing a business plan, and the like. A researcher wants to
conduct a similar study to compare the results between two industries: the computer hardware industry
and the banking industry. He takes a random sample of 56 computer firms and 89 banks. The
researcher asks whether market testing is the most difficult activity to accomplish in developing a new
product. Some 48% of the sampled computer companies and 56% of the sampled banks respond that it
is the most difficult activity. Use a level of significance of 0.20 to test whether there is a significant
difference in the responses to the question from these two industries.
.Exercise #8
One recent study showed that the average annual amount spent by an East Coast household on
frankfurters was $23.84 compared with an average of $19.83 for West Coast households. Suppose a
random sample of 12 East Coast households showed that the standard deviation of these purchases
(frankfurters) was $7.52, whereas a random sample of 15 West Coast households resulted in a
standard deviation of $6.08. Do these samples provide enough evidence to conclude that the variance
of annual frankfurter purchases for East Coast households is greater than the variance of annual
frankfurter purchases for West Coast households? Let alpha be 0.05. Assume amounts spent per year
on frankfurters are normally distributed.

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Course Title: Business Statistics II

2- Estimate the confidence Interval for the difference. Interpret

According to Runzheimer International, a family of four in Manhattan with $60,000 annual

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