Statistics & Research Methods
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FINAL EXAMINATION
Instruction : Please answer the following questions. All questions carry equal marks.
1. A manufacturer of power tools claims that the mean amount of time required to assemble their top-ofthe-
line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of
64 purchasers of this table saw is taken. The probability that the sample mean will be greater than 88
minutes is ________.
TABLE 7-2
The time spent studying by students in the week before final exams follows a normal distribution with a
standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean
study time for the population of all students.
2. Referring to Table 7-2, what is the probability that the sample mean is more than 3 hours below the
population mean?
TABLE 7-5
According to a survey, only 15% of customers who visited the website of a major retail store made a
purchase. Random samples of size 50 are selected.
3. Referring to Table 7-5, the standard deviation of all the sample proportions of customers who will
make a purchase after visiting the website is ________.
TABLE 7-7
Online customer service is a key element to successful online retailing. According to a marketing survey,
37.5% of online customers take advantage of the online customer service. Random samples of 200
customers are selected.
Referring to Table 7-7, 95% of the samples proportions symmetrically around the population
proportion will have between ________ % and ________ % of the customers who take advantage of
online customer service.
TABLE 8-7
A hotel chain wants to estimate the mean number of rooms rented daily in a given month. The population
of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of
24 rooms. During February, a sample of 25 days has a sample mean of 37 rooms.
5. Referring to Table 8-7, the sampling error of a 99% confidence interval for the mean number of
rooms rented daily in a given month is ________.
Statistics & Research Methods – Final Exam BUS506 (2011E)
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TABLE 8-8
The president of a university would like to estimate the proportion of the student population that owns a
personal computer. In a sample of 500 students, 417 own a personal computer.
6. Referring to Table 8-8, the sampling error of a 99% confidence interval for the proportion of the
student population who own a personal computer is ________.
TABLE 8-11
A university wanted to find out the percentage of students who felt comfortable reporting cheating by
their fellow students. A survey of 2,800 students was conducted and the students were asked if they felt
comfortable reporting cheating by their fellow students. The results were 1,344 answered “Yes” and 1,456
answered “No.”
7. Referring to Table 8-11, the sampling error of a 99% confidence interval for the proportion of student
population who feel comfortable reporting cheating by their fellow students is ________.
TABLE 8-14
A poll was conducted by the marketing department of a video game company to determine the popularity
of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young
adults were conducted which revealed that 49% said they would purchase the new game. The margin of
error was ±3 percentage points.
8. Referring to Table 8-14, what is the needed sample size to obtain a 90% confidence interval estimate
of the percentage of the targeted young adults who will purchase the new game by allowing the same
level of margin of error?
TABLE 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses. Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time. When a person is an agriculture major,
the student will incorrectly identify that person as a business major 16% of the time. Presented with one
person and asked to identify the major of this person (who is either a business or an agriculture major), he
considers this to be a hypothesis test with the null hypothesis being that the person is a business major and
the alternative that the person is an agriculture major.
9. Referring to Table 9-2, what would be a Type II error?
A) Saying that the person is a business major when in fact the person is a business major
B) Saying that the person is a business major when in fact the person is an agriculture major
C) Saying that the person is an agriculture major when in fact the person is a business major
D) Saying that the person is an agriculture major when in fact the person is an agriculture major
Statistics & Research Methods – Final Exam BUS506 (2011E)
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TABLE 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean
of no more than 250 W. From previous studies, it is believed that power consumption for microwave
ovens is normally distributed with a population standard deviation of 15 W. A consumer group has
decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find
that they consume a mean of 257.3 W.
10. Referring to Table 9-3, the p-value of the test is ________.
TABLE 9-7
A major home improvement store conducted its biggest brand recognition campaign in the company’s
history. A series of new television advertisements featuring well-known entertainers and sports figures
was launched. A key metric for the success of television advertisements is the proportion of viewers who
“like the ads a lot.” A study of 1,189 adults who viewed the ads reported that 230 indicated that they “like
the ads a lot.” The percentage of a typical television advertisement receiving the “like the ads a lot” score
is believed to be 22%. Company officials wanted to know if there is evidence that the series of television
advertisements are less successful than the typical ad (i.e. if there is evidence that the population
proportion of “like the ads a lot” for the company’s ads is less than 0.22) at a 0.01 level of significance.
11. Referring to Table 9-7, the largest level of significance at which the null hypothesis will not be
rejected is ________.
TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the
entering class from previous years but their mean SAT score is lower than previous years. He took a
sample of 20 of this year’s entering students and found that their mean SAT score is 1,501 with a standard
deviation of 53. The university’s record indicates that the mean SAT score for entering students from
previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of
significance.
12. Referring to Table 9-9, the highest level of significance at which the null hypothesis cannot be
rejected is ________.
13. The Wall Street Journal recently ran an article indicating differences in perception of sexual
harassment on the job between men and women. The article claimed that women perceived the
problem to be much more prevalent than did men. One question asked to both men and women was:
“Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the
men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were
interviewed. Construct a 99% confidence interval estimate of the difference between the proportion of
women and men who think sexual harassment is a major problem in the American workplace.
Statistics & Research Methods – Final Exam BUS506 (2011E)
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TABLE 10-9
The following Excel output contains the results of a test to determine whether the proportions of satisfied
customers at two resorts are the same or different.
14. Referring to Table 10-9, construct a 95% confidence interval estimate of the difference in the
population proportion of satisfied guests between the two resorts.
TABLE 10-12
A quality control engineer is in charge of the manufacture of computer disks. Two different processes can
be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of
defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that
27 and 18 of them, respectively, are defective. If Kohler is designated as “Group 1″ and Russell is
designated as “Group 2,” perform the appropriate test at a level of significance of 0.01.
15. Referring to Table 10-12, construct a 95% confidence interval estimate of the difference in proportion
between the Kohler and Russell disks that are defective.
Statistics & Research Methods – Final Exam BUS506 (2011E)
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TABLE 10-13
The amount of time required to reach a customer service representative has a huge impact on customer
satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the
mean amounts of time required to reach a customer service representative between two hotels. Assume
that the population variances in the amount of time for the two hotels are not equal.
16. Referring to Table 10-13, what is the smallest level of significance at which the null hypothesis will
still not be rejected?
A) 0.05
B) 0.10
C) 0.3625
D) 0.7250
TABLE 11-6
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties
of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre.
Treating this as a randomized block design, the results are presented in the table that follows.
Fields Smith Walsh Trevor
1 11.1 19.0 14.6
2 13.5 18.0 15.7
3 15.3 19.8 16.8
4 14.6 19.6 16.7
5 9.8 16.6 15.2
17. Referring to Table 11-6, the among-group variation or SSA is ________.
Statistics & Research Methods – Final Exam BUS506 (2011E)
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TABLE 11-7
A student team in a business statistics course designed an experiment to investigate whether the brand of
bubblegum used affected the size of bubbles they could blow. To reduce the person-to-person variability,
the students decided to use a randomized block design using themselves as blocks. Four brands of
bubblegum were tested. A student chewed two pieces of a brand of gum and then blew a bubble,
attempting to make it as big as possible. Another student measured the diameter of the bubble at its
biggest point. The following table gives the diameters of the bubbles (in inches) for the 16 observations.
18. Referring to Table 11-7, the amount of total variation or SST is ________.
TABLE 11-9
Psychologists have found that people are generally reluctant to transmit bad news to their peers. This
phenomenon has been termed the “MUM effect.” To investigate the cause of the MUM effect, 40
undergraduates at Duke University participated in an experiment. Each subject was asked to administer an
IQ test to another student and then provide the test taker with his or her percentile score. Unknown to the
subject, the test taker was a bogus student who was working with the researchers. The experimenters
manipulated two factors: subject visibility and success of test taker, each at two levels. Subject visibility
was either visible or not visible to the test taker. Success of the test taker was either top 20% or bottom
20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions, then the
time (in seconds) between the end of the test and the delivery of the percentile score from the subject to
the test taker was measured. (This variable is called the latency to feedback.) The data were subjected to
appropriate analyses with the following results.
Source df SS MS F PR > F
Subject visibility 1 1380.24 1380.24 4.26 0.043
Test taker success 1 1325.16 1325.16 4.09 0.050
Interaction 1 3385.80 3385.80 10.45 0.002
Error 36 11,664.00 324.00
Total 39 17,755.20
19. Referring to Table 11-9, at the 0.01 level, what conclusions can you reach from the analysis?
A) At the 0.01 level, subject visibility and test taker success are significant predictors of latency
feedback.
B) At the 0.01 level, the model is not useful for predicting latency to feedback.
C) At the 0.01 level, there is evidence to indicate that subject visibility and test taker success interact.
D) At the 0.01 level, there is no evidence of interaction between subject visibility and test taker
success.
Statistics & Research Methods – Final Exam BUS506 (2011E)
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TABLE 11-11
A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show
the benefits of managed health care to an insurance company. The physician believes that certain types of
doctors are more cost-effective than others. One theory is that primary specialty is an important factor in
measuring the cost-effectiveness of physicians. To investigate this, the president obtained independent
random samples of 20 HMO physicians from each of 4 primary specialties General Practic e (GP),
Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) and recorded the total charges
per member per month for each. A second factor which the president believes influences total charges per
member per month is whether the doctor is a foreign or US medical school graduate. The president
theorizes that foreign graduates will have higher mean charges than US graduates. To investigate this, the
president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty
types described above. So information on charges for 40 doctors (20 foreign and 20 US medical school
graduates) was obtained for each of the 4 specialties. The results for the ANOVA are summarized in the
following table.
Source df SS MS F PR > F
Specialty 3 22,855 7,618 60.94 0.0001
Med school 1 105 105 0.84 0.6744
Interaction 3 890 297 2.38 0.1348
Error 152 18,950
Total 159 42,800
20. Referring to Table 11-11, what assumption(s) need(s) to be made in order to conduct the test for
differences between the mean charges of foreign and US medical school graduates?
A) There is no significant interaction effect between the area of primary specialty and the medical
school on the doctors’ mean charges.
B) The charges in each group of doctors sampled are drawn from normally distributed populations.
C) The charges in each group of doctors sampled are drawn from populations with equal variances.
D) All of the above are necessary assumptions.
TABLE 12-10
One criterion used to evaluate employees in the assembly section of a large factory is the number of
defective pieces per 1,000 parts produced. The quality control department wants to find out whether there
is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial
training period any improvement due to a learning effect might be offset by a loss of motivation. A defect
rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table
below.
Years Since Training Period
< 1 Year 1-4 Years 5-9 Years
6 9 9
9 19 23
High
Defect Rate: Average
Low 7 8 10
Statistics & Research Methods – Final Exam BUS506 (2011E)
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21. Referring to Table 12-10, what is the expected number of employees with 1 to 4 years of training time
and a high defect rate?
A) 12.00
B) 8.64
C) 6.67
D) 6.00
TABLE 12-14
The director of transportation of a large company is interested in the usage of the company’s van pool
program. She surveyed 129 of her employees on the usage of the program before and after a campaign to
convince her employees to use the service and obtained the following:
She will use this information to perform test using a level of significance of 0.05.
22. Referring to Table 12-14, the director now wants to know if the proportion of employees who use the
service before the campaign and the proportion of employees who use the service after the campaign
are the same. What is the p-value of the test statistic using a 5% level of significance?
23. A local real estate appraiser analyzed the sales prices of homes in 2 neighborhoods to the
corresponding appraised values of the homes. The goal of the analysis was to compare the
distribution of sale-to-appraised ratios from homes in the 2 neighborhoods. Random and independent
samples were selected from the 2 neighborhoods from last year’s homes sales, 8 from each of the 2
neighborhoods. Identify the nonparametric method that would be used to analyze the data.
A) X2-test for the differences among more than two proportions
B) McNemar test for the difference between two proportions
C) the Wilcoxon rank sum test, using the test statistic T1
D) X2-test for the variance
TABLE 12-19
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds.
The results are presented in miles per hour in the table below.
Trial Barth Tornado Reiser Shaw
1 43 37 41 43
2 46 38 45 45
3 43 39 42 46
24. Referring to Table 12-19, the calculated value of the Kruskal-Wallis test statistic H is ________.
Statistics & Research Methods – Final Exam BUS506 (2011E)
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TABLE 12-20
Three new different models of compact SUVs have just arrived at the market. You are interested in
comparing the gas mileage performance of all three models to see if they are the same. A partial computer
output for twelve compact SUVs of each model is given below:
You are told that the gas mileage population distributions for all three models are not normally distributed.
25. Referring to Table 12-20, what is the critical value of the Kruskal-Wallis test statistic?
TABLE 13-4
The managers of a brokerage firm are interested in finding out if the number of new clients a broker
brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the
number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars.
These data are presented in the table that follows.
Broker Clients Sales
1 27 52
2 11 37
3 42 64
4 33 55
5 15 29
6 15 34
7 25 58
8 36 59
9 28 44
10 30 48
11 17 31
12 22 38
26. Referring to Table 13-4, the regression sum of squares (SSR) is ________.
27. If the Durbin-Watson statistic has a value close to 4, which assumption is violated?
A) Normality of the errors
B) Independence of errors
C) Homoscedasticity
D) None of the above
Statistics & Research Methods – Final Exam BUS506 (2011E)
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TABLE 13-7
An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the
market index like the S&P 500, then it is possible to reduce the variability of the portfolio’s return. In
other words, one can create a portfolio with positive returns but less exposure to risk.
A sample of 26 years of S&P 500 index and a portfolio consisting of stocks of private prisons, which are
believed to be negatively related to the S&P 500 index, is collected. A regression analysis was performed
by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 index (X) to prove
that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance.
The results are given in the following Excel output.
Coefficients Standard Error T Stat p-value
Intercept
S &P
4.8660
-0.5025
0.3574
0.0716
13.6136
-7.0186
8.7932E-13
2.94942E-07
Note: 2.94942E-07 = 2.94942*10-7
28. Referring to Table 13-7, to test whether the prison stocks portfolio is negatively related to the S&P
500 index, the p-value of the associated test statistic is
A) 2.94942E-07.
B) 2.94942E-07/2.
C) (2.94942E-07)2.
D) 8.7932E-13.
TABLE 13-10
The management of a chain electronic store would like to develop a model for predicting the weekly sales
(in thousands of dollars) for individual stores based on the number of customers who made purchases. A
random sample of 12 stores yields the following results:
Customers Sales (Thousands of Dollars)
907 11.20
926 11.05
713 8.21
741 9.21
780 9.42
898 10.08
510 6.73
529 7.02
460 6.12
872 9.52
650 7.53
603 7.25
29. Referring to Table 13-10, what is the value of the coefficient of determination?
Statistics & Research Methods – Final Exam BUS506 (2011E)
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TABLE 13-12
The manager of the purchasing department of a large saving and loan organization would like to develop
a model to predict the amount of time (measured in hours) it takes to record a loan application. Data are
collected from a sample of 30 days, and the number of applications recorded and completion time in
hours is recorded. Below is the regression output:
Note: 4.3946E-15 is 4.3946 ×
Statistics & Research Methods – Final Exam BUS506 (2011E)
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30. Referring to Table 13-12, the degrees of freedom for the t test on whether the number of loan
applications recorded affects the amount of time are
A) 1.
B) 28.
C) 29.
D) 30.
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