The topic of "Statistics & Research Methods"
1. A manufacturer of power tools claims that the mean amount of time required to assemble their top-of- the-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.
2. 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.
3. 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."
4. 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 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.
5. 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.
6. Referring to Table 9-7, the largest level of significance at which the null hypothesis will not be rejected is .
7. 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.
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.
8. 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
|
9. 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.
| 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 |
0.05 |
| Interaction |
1 |
3385.8 |
3385.8 |
10.45 |
0.002 |
| Error |
36 |
11,664.00 |
324 |
|
|
| Total |
39 |
17,755.20 |
|
|
|
10. 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
|
|
High
Defect Rate: Average
Low
|
< 1 Year
|
1-4 Years
|
5-9 Years
|
|
6
|
9
|
9
|
|
9
|
19
|
23
|
|
7
|
8
|
10
|
11. 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
12. 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:
| Kruskal-Wallis rank test for diffrences in medians |
|
| Data |
|
| Level of siginificance |
0.5 |
|
|
| Intermediate Caluclation |
|
| Sum of sqared Ranks/Samples Size |
15123.04 |
| Sum of sample sizes |
36 |
| Number of Groups |
3 |
| Group |
Sample Size |
Sum of Ranks |
Mean Ranks |
Square of sum of ranks |
| 1 |
12 |
185.5 |
15.458333 |
34410.25 |
| 2 |
12 |
114.5 |
9.5416667 |
13110.25 |
| 3 |
12 |
366 |
30.5 |
133956 |
You are told that the gas mileage population distributions for all three models are not normally distributed.
13. Referring to Table 12-20, what is the critical value of the Kruskal-Wallis test statistic?
14. 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
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
|
15. Referring to Table 13-10, what is the value of the coefficient of determination?
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