# Statistics and Research Methods

**Paper , Order, or Assignment Requirements**

Answer all the questions

FINAL ASSIGNMENT

Instruction : Please answer ALL questions. All questions carry equal marks. Do

not write over 2000 words for the entire assignment.

- 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 7-5

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.

- 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 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.

- 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 ________.

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.”

- 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 ________.

Statistics & Research Methods – Final Assignment BUS506 (2015A)

Page 2

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.

- 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

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.

- Referring to Table 9-7, the largest level of significance at which the null hypothesis will not be

rejected is ________.

- 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 Assignment BUS506 (2015A)

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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.

- 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.

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

- Referring to Table 11-6, the among-group variation or SSA 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.

Statistics & Research Methods – Final Assignment BUS506 (2015A)

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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

- 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.

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

- 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

Statistics & Research Methods – Final Assignment BUS506 (2015A)

Page 5

- 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 12-20

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.

- Referring to Table 12-20, what is the critical value of the Kruskal-Wallis test statistic?
- 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 Assignment BUS506 (2015A)

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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

- Referring to Table 13-10, what is the value of the coefficient of determination?

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