Stat 125 | Mathematics

Q1. Which of the following is true regarding the sampling distribution of the mean for a large sample size?
a. It has the same shape, mean, and standard deviation as the population.
b. It has a normal distribution with the same mean and standard deviation as the population.
c. It has the same shape and mean as the population, but has a smaller standard deviation.
d. It has a normal distribution with the same mean as the population but with a smaller standard deviation.

Q2. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over \$25,000 is 80%. Of the households surveyed, 60% had incomes over \$25,000 and 70% had 2 cars. The probability that annual household income is over \$25,000 if the residents of a household do not own 2 cars is:
a. 0.12
b. 0.18
c. 0.40
d. 0.55

Q3. The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of:
a. inferential statistics.
b. descriptive statistics.
c. a parameter.
d. a statistic.

Q4. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day.

If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant to use 25 days of data to construct the interval estimate, what confidence level can she attach to the interval estimate?
a. 99.7%
b. 99.0%
c. 98.0%
d. 95.4%

Q5. Referring to the histogram, how many graduating seniors attended the luncheon?

a. 4
b. 152
c. 275
d. 388

Q6. The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15

0.15

15 but less than 20

0.10

20 but less than 25

0.07

25 but less than 30

0.07

30 or more

0.02

Referring to the table, if 10 calls lasted 30 minutes or more, how many calls lasted less than 5 minutes?
a. 10
b. 185
c. 295
d. 500

Q7. The collection of all possible events is called:
a. a simple probability.
b. a sample space.
c. a joint probability.
d. the null set.

Q8. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution:

Price:

\$10.00

\$12.50

\$15.00

Probability:

0.35

0.40

0.25

How much should the lab budget for next year’s rat orders be, assuming this distribution does not change?
a. \$520
b. \$637
c. \$650
d. \$780

Q9. A professor of economics at a small Texas university wanted to determine what year in school students were taking his tough economics course. Shown below is a pie chart of the results. What percentage of the class took the course prior to reaching their senior year?

a. 14%
b. 44%
c. 54%
d. 86%

Q10. Since a _______ is not a randomly selected probability sample, there is no way to know how well it represents the overall population.
a. simple random sample
b. quota sample
c. stratified sample
d. cluster sample

Q11. A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the population from which the study was sampled.
a. The 250 randomly selected adult American pine trees in the forest.
b. The 25,000 adult American pine trees in the forest.
c. All the adult American pine trees taller than 60 feet in the world.
d. All American pine trees, of any age, in the forest.

Q12. A population frame for a survey contains a listing of 72,345 names. Using a table of random numbers, how many digits will the code numbers for each member of your population contain?
a. 3
b. 4
c. 5
d. 6

Q13. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the portion of students at her university who visited campus bars every weekend. Her advisor took a random sample of 250 students. The portion of students in the sample who visited campus bars every weekend is an example of a __________.
a. categorical random variable
b. discrete random variable
c. parameter
d. statistic

Q14. The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15

0.15

15 but less than 20

0.10

20 but less than 25

0.07

25 but less than 30

0.07

30 or more

0.02

Referring to Table 2-5, if 100 calls were randomly sampled, how many calls lasted 15 minutes or longer?
a. 10
b. 14
c. 26
d. 74

Q15. If two events are mutually exclusive, what is the probability that one or the other occurs?
a. 0
b. 0.50
c. 1.00
d. Cannot be determined from the information given.

Q16. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over \$25,000 is 80%. Of the households surveyed, 60% had incomes over \$25,000 and 70% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over \$25,000 a year is:
a. 0.12
b. 0.18
c. 0.22
d. 0.48

Q17. If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs?
a. 0.
b. 0.50.
c. 1.00.
d. Cannot be determined from the information given.

Q18. Why is the Central Limit Theorem so important to the study of sampling distributions?
a. It allows us to disregard the size of the sample selected when the population is not normal.
b. It allows us to disregard the shape of the sampling distribution when the size of the population is large.
c. It allows us to disregard the size of the population we are sampling from.
d. It allows us to disregard the shape of the population whennis large.

Q19. A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result.

Did Well on Midterm

Did Poorly on Midterm

Studying for Exam

80

20

Went Bar Hopping

30

70

Referring to the table, of those who did well on the midterm in the sample, _______ percent of them went bar hopping the weekend before the midterm.
a. 15
b. 27.27
c. 30
d. 50

Q20. Tim was planning for a meeting with his boss to discuss a raise in his annual salary. In preparation, he wanted to use the Consumer Price Index to determine the percentage increase in his salary in terms of real income over the last three years. Which method of data collection was involved when he used the Consumer Price Index?
a. Published sources
b. Experimentation
c. Surveying
d. Observation

Q21. A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below.

Stem

Leaves

3

24

4

3478999

5

112345

6

12566

7

1

8

9

2

Referring to the table, what percentage of the respondents rated overall television quality with a rating between 50 and 75?
a. 0.11
b. 0.40
c. 0.44
d. 0.56

Q22. The process of using sample statistics to draw conclusions about true population parameters is called:
a. statistical inference.
b. the scientific method.
c. sampling.
d. descriptive statistics.

Q23. If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?
a. 0
b. 0.50
c. 1.00
d. Cannot be determined from the information given.

Q24. Which of the following is most likely a parameter as opposed to a statistic?
a. The average score of the first five students completing an assignment.
b. The proportion of females registered to vote in a county.
c. The average height of people randomly selected from a database.
d. The proportion of trucks stopped yesterday that were cited for bad brakes.

Q25. Selection of raffle tickets from a large bowl is an example of:
a. sampling with replacement.
b. sampling without replacement.
c. subjective probability.
d. None of the above.

Q26. The portfolio expected return of two investments
a. will be higher when the covariance is zero.
b. will be higher when the covariance is negative.
c. will be higher when the covariance is positive.
d. does not depend on the covariance.

Q27. Given the numbers: 1, 3, 5, 7, 8 what are the average and the median?
a. Average = 4.8; Median = 5.0
b. Average = 5.0; Median = 5.0
c. Average = 4.8; Median = 4.8
d. Average = 5.0; Median = 4.8

Q28. The employees of a company were surveyed on questions regarding their educational background and marital status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is:
a. 0.10
b. 0.25
c. 0.667
d. 0.733

Q29. A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?
a. 0.86466
b. 0.60653
c. 0.39347
d. 0.13534

Q30. The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15

0.15

15 but less than 20

0.10

20 but less than 25

0.07

25 but less than 30

0.07

30 or more

0.02

Referring to the table, what is the width of each class?
a. 1 minute
b. 5 minutes
c. 2%
d. 100%

Q31. The probability that
·         house sales will increase in the next 6 months is estimated to be 0.25.
·         the interest rates on housing loans will go up in the same period is estimated to be 0.74
·         house sales or interest rates will go up during the next 6 months is estimated to be 0.89
The probability that house sales will increase but interest rates will not during the next 6 months is:

a. 0.065
b. 0.15
c. 0.51
d. 0.89

Q32. Which of the mean, median, mode, and geometric mean are resistant measures of central tendency?
a. The mean and median.
b. The median and mode.
c. The mode and geometric mean.
d. The mean and mode.

Q33. The probability that
·         house sales will increase in the next 6 months is estimated to be 0.25
·         the interest rates on housing loans will go up in the same period is estimated to be 0.74
·         house sales or interest rates will go up during the next 6 months is estimated to be 0.89
The probability that neither house sales nor interest rates will increase during the next 6 months is:
a. 0.11
b. 0.195
c. 0.89
d. 0.90

Q34. Which of the following statistics is not a measure of central tendency?
a. Mean.
b. Median.
c. Mode.
d. Q3.

Q35. The width of each bar in a histogram corresponds to the:
a. differences between the boundaries of the class.
b. number of observations in each class.
c. midpoint of each class.
d. percentage of observations in each class.

Q36. In left-skewed distributions, which of the following is the correct statement?
a. The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3.
b. The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation.
c. The distance from the smallest observation to Q2 is smaller than the distance from Q2 to the largest observation.
d. The distance from Q1 to Q3 is twice the distance from Q1 to Q2.

Q37. The Central Limit Theorem is important in statistics because:
a. for a largen, it says the population is approximately normal.
b. for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.
c. for a largen, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.
d. for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Q38. A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result.

Did Well on the midterm

Did Poorly on Midterm

Studying for Exam

80

20

Went Bar Hopping

30

70

Referring to the table, _______ percent of the students in the sample went bar hopping the weekend before the midterm and did well on the midterm.
a. 15
b. 27.27
c. 30
d. 50

Q39. Which of the following statements about the median is not true?
a. It is more affected by extreme values than the mean.
b. It is a measure of central tendency.
c. It is equal to Q2.
d. It is equal to the mode in bell-shaped “normal” distributions.

Q40. A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?
a. No, and we are 90% sure of it.
b. No. The proportion is 54.17%.
c. Maybe. 0.60 is a believable value of the population proportion based on the information above.

Q1. The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H0: ρ = 0 against the two-sided alternative H1: ρ ≠ 0. To test H0: ρ = 0 against the one-sided alternative H1: ρ > 0 at a significance level of 0.193, the p-value is    a. 0.256/2    b. 0.256    c. 1 – 0.256    d. 1 – 0.256/2
Q2. A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Size

Mean

Std Dev

Females

18

48,266.7

13,577.63

Males

12

55,000

11,741.29

Std Error = 4,764.82

Means Diff = -6,733.3

Z = -1.4528 2-tailed p value = 0.1463

T = -1.4221 2-tailed p value = 0.1574

Referring to the table, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?    a. Both populations of salaries (male and female) must have approximate normal distributions.    b. The population variances are approximately equal.    c. The samples were randomly and independently selected.    d. All of the above assumptions were necessary.
Q3. The Y-intercept (b0) represents the:    a. predicted value of Y when X = 0.    b. change in estimated average Y per unit change in X.    c. predicted value of Y.    d. variation around the sample regression line.
Q4. 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. the Wilcoxon Signed-Ranks Test, using the test statistic Z    b. the Wilcoxon Signed-Ranks Test, using the test statistic W    c. the Wilcoxon Rank Sum Test, using the test statistic T1    d. the Wilcoxon Rank Sum Test, using the test statistic Z
Q5. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:    a. -4.12    b. -2.33    c. -1.86    d. -0.07
Q6. A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (W, X, Y, and Z). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
W: 1.2, 1.1, 0.9, 0.4X: 2.5, 2.1, 1.9, 1.6Y: 1.0, 1.5, 1.1, 1.3Z: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table:

Source

df

SS

MS

F

PR > F

Neighborhoods

2.97

0.990

8.31

0.0260

Error

12

Total

4.40

Referring to the table, the within group mean squares is    a. 0.119    b. 0.990    c. 1.109    d. 8.31
Q7. If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to:    a. autocorrelation.    b. the presence of dummy variables.    c. the absence of dummy variables.    d. collinearity.
Q8. In a multiple regression model, the adjusted r2    a. cannot be negative.    b. can sometimes be negative.    c. can sometimes be greater than +1.    d. has to fall between 0 and +1.
Q9. Why would you use the Tukey-Kramer procedure?    a. To test for normality.    b. To test for homogeneity of variance.    c. To test independence of errors.    d. To test for differences in pairwise means.
Q10. A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. How should the data be analyzed?

Starting Room

Interior

Exterior

Wall Signs

141

224

119

339

238

139

Map

85

226

94

129

126

130

a. Completely randomized design    b. Randomized block design    c. 2 x 2 factorial design    d. Kruskal-Wallis rank test
Q11. As a business statistics project, a student examined the factors that determine parking meter rates throughout the campus and downtown area. The campus is a group of buildings located in the center of downtown, with an open central quadrangle. Data were collected for the price of parking per hour and the number of blocks to the quadrangle. In addition, two dummy variables were coded to indicate the location of the parking meter (See below). The population regression model hypothesized is
Yi = ß0 + ß1x1i + ß2x2i + ß3x3i + ei
where Y is the price per hourx1 is a numerical variable = the number of blocks to the quadrangle(Note that if x1 is less than 2, then the meter is on campus; if x1 is less than 3, then the meter is downtown)x2 is a dummy variable = 1 if inside downtown and off campus, 0 otherwisex3 is a dummy variable = 1 if outside downtown and off campus, 0 otherwise
The following Excel results are obtained.

Regression Statistics

Multiple R

9.9659

R Square

0.9331

0.9294

Standard Error

0.0327

Observations

58

ANOVA

df

SS

MS

F

Signif F

Regression

3

0.8094

0.2698

251.1995

1.0964E-31

Residual

54

0.0580

0.0010

Total

57

0.8675

Coeff

StdError

t Stat

P-value

Intercept

0.5118

0.0136

37.4675

2.4904

X1

-0.0045

0.0034

-1.3275

0.1898

X2

-0.2392

0.0123

-19.3942

5.3581E-26

X3

-0.0002

0.0123

-0.0214

0.9829

Referring to the tables, predict the meter rate per hour if one parks outside of downtown and off campus, 3 blocks from the quad.     a. \$-0.0139    b. \$0.2589    c. \$0.2604    d. \$0.4981
Q12. If we use the chi-squared method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to:    a. 3    b. 4    c. 5    d. 1
Q13. An economist is interested to see how consumption for an economy (in \$ billions) is influenced by gross domestic product (\$ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT

Regression Statistics

Multiple R

0.991

R Square

0.982

0.976

Standard Error

0.299

Observations

10

ANOVA

df

SS

MS

F

Signif F

Regression

2

33.4163

16.7082

186.325

0.0001

Residual

7

0.6277

0.0897

Total

9

34.0440

Coeff

StdError

t Stat

P-value

Intercept

-0.0861

0.5674

-0.152

0.8837

GDP

0.7654

0.0574

13.340

0.0001

Price

-0.0006

0.0028

-0.219

0.8330

Referring to the tables, one economy in the sample had an aggregate consumption level of \$4 billion, a GDP of \$6 billion, and an aggregate price level of 200. What is the residual for this data point?     a. \$4.39 billion    b. \$0.39 billion    c. -\$0.39 billion    d. -\$1.33 billion
Q14. Testing for the existence of correlation is equivalent to    a. testing for the existence of the slope (β1).    b. testing for the existence of the Y-intercept (β0).    c. the confidence interval estimate for predicting Y.    d. testing for the existence of the slope (β10).
Q15. As a business statistics project, a student examined the factors that determine parking meter rates throughout the campus and downtown area. The campus is a group of buildings located in the center of downtown, with an open central quadrangle. Data were collected for the price of parking per hour and the number of blocks to the quadrangle. In addition, two dummy variables were coded to indicate the location of the parking meter (See below). The population regression model hypothesized is
Yi = ß0 + ß1x1i + ß2x2i + ß3x3i + ei
where Y is the price per hourx1 is a numerical variable = the number of blocks to the quadrangle(Note that if x1 is less than 2, then the meter is on campus; if x1 is less than 3, then the meter is downtown)x2 is a dummy variable = 1 if inside downtown and off campus, 0 otherwisex3 is a dummy variable = 1 if outside downtown and off campus, 0 otherwise
The following Excel results are obtained.

Regression Statistics

Multiple R

9.9659

R Square

0.9331

0.9294

Standard Error

0.0327

Observations

58

ANOVA

df

SS

MS

F

Signif F

Regression

3

0.8094

0.2698

251.1995

1.0964E-31

Residual

54

0.0580

0.0010

Total

57

0.8675

Coeff

StdError

t Stat

P-value

Intercept

0.5118

0.0136

37.4675

2.4904

X1

-0.0045

0.0034

-1.3275

0.1898

X2

-0.2392

0.0123

-19.3942

5.3581E-26

X3

-0.0002

0.0123

-0.0214

0.9829

Referring to the tables, if one is already outside of downtown and off campus but decides to park an additional 3 blocks from the quadrangle, the estimated average parking meter rate will:     a. decrease by 0.0045.    b. decrease by 0.0135.    c. decrease by 0.0139.    d. decrease by 0.4979.
Q16. The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.
Hypothesized Difference0Level of Significance 0.05Group 1Number of Successes163Sample Size227Group 2Number of Successes154Sample Size262Group 1 Proportion0.718061674Group 2 Proportion0.58778626Difference in Two Proportions 0.130275414Average Proportion0.648261759Test Statistic3.00875353Two-Tailed TestLower Critical Value -1.959961082Upper Critical Value 1.959961082p-Value 0.002623357
Referring to the data above, if you want to test the claim that “Resort 1 (Group 1) has a higher proportion of satisfied guests compared to Resort 2 (Group 2),” the p-value of the test will be    a. 0.00262    b. 0.00262/2    c. 2*(0.00262)    d. 1 – (0.00262/2)
Q17. A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the µltiple regression. Microsoft Excel output is provided below:
SUMMARY OUTPUT

Regression Statistics

Multiple R

0.865

R Square

0.748

0.726

Standard Error

5.195

Observations

50

ANOVA

df

SS

MS

F

Signif F

Regression

3605.7736

901.4434

0.0001

Residual

1214.2264

26.9828

Total

49

4820.0000

Coeff

StdError

t Stat

P-value

Intercept

-1.6335

5.8078

-0.281

0.7798

Income

0.4485

0.1137

3.9545

0.0003

Size

4.2615

0.8062

5.286

0.0001

School

-0.6517

0.4319

-1.509

0.1383

Referring to the tables, one individual in the sample had an annual income of \$10,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet) for this data point?    a. 8.10    b. 5.40    c. -5.40    d. -8.10
Q18. A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following:

Employee

Y

X1

X2

1

100

10

7

2

90

3

10

3

80

8

9

4

70

5

4

5

60

5

8

6

50

7

5

7

40

1

4

8

30

1

1

Referring to the table, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b1?    a. 0.998    b. 3.103    c. 4.698    d. 21.293

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 the table, in the context of this study, interpret the statement: “Subject visibility and test taker success interact.”     a. The difference between the mean feedback time for visible and nonvisible subjects depends on the success of the test taker.    b. The difference between the mean feedback time for test takers scoring in the top 20% and bottom 20% depends on the visibility of the subject.    c. The relationship between feedback time and subject visibility depends on the success of the test taker.    d. All of the above are correct interpretations.
Q25. A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:

City

Price (\$)

Sales

River Falls

1.30

100

Hudson

1.60

90

Ellsworth

1.80

90

Prescott

2.00

40

Rock Elm

2.40

38

Stillwater

2.90

32

Referring to the table, what is the coefficient of correlation for these data?    a. -0.8854    b. -0.7839    c. 0.7839    d. 0.8854
Q26. A ____________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.    a. significance level    b. critical value    c. test statistic    d. parameter
Q27. An investment specialist claims that if one holds a portfolio that moves in 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 private prisons stock 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

4.866004258

0.35743609

13.61363441

8.7932E-13

S&P

-0.502513506

0.071597152

-7.01862425

2.94942E-07

Referring to the table, which of the following will be a correct conclusion?    a. We cannot reject the null hypothesis and, therefore, conclude that there is sufficient evidence to show that the prison stock portfolio and S&P 500 index are negatively related.    b. We can reject the null hypothesis and, therefore, conclude that there is sufficient evidence to show that the prison stock portfolio and S&P 500 index are negatively related.    c. We cannot reject the null hypothesis and, therefore, conclude that there is not sufficient evidence to show that the prison stock portfolio and S&P 500 index are negatively related.    d. We can reject the null hypothesis and conclude that there is not sufficient evidence to show that the prison stock portfolio and S&P 500 index are negatively related.
Q28. 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 Defect Rate High 6 9 9 Average 9 19 23 Low 7 8 10 Referring to the table, find the rejection region necessary for testing at the 0.05 level of significance whether there is a relationship between defect rate and years of experience.    a. Reject H0 if chi-square > 16.919     b. Reject H0 if chi-square > 15.507     c. Reject H0 if chi-square > 11.143     d. Reject H0 if chi-square > 9.488
Q29. A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. An Excel output of the appropriate analysis is given below:

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Signs

14008.33

14008.33

0.11267

5.317645

Starting Location

12288

2.784395

0.13374

5.317645

Interaction

48

48

0.919506

5.317645

Within

35305.33

4413.167

Total

61649.67

11

Referring to the table, the within (error) degrees of freedom is    a. 1    b. 4    c. 8    d. 11
Q30. If we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2, the appropriate test to use is    a. the Z test.    b. the chi-squared test.    c. the W test.    d. the X test.
Q31. A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Size

Mean

Std Dev

Females

18

48,266.7

13,577.63

Males

12

55,000

11,741.29

Std Error = 4,764.82

Means Diff = -6,733.3

Z = -1.4528 2-tailed p value = 0.1463

T = -1.4221 2-tailed p value = 0.1574

Referring to the table, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in the table, the correct test statistic is:    a. 4,634.72    b. -1.4221    c. -1.4528    d. -6,733.33
Q32. If we are performing a two-tailed test of whether μ = 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.    a. less than    b. greater than    c. equal to    d. not comparable to
Q33. Parents complain that children read too few storybooks and watch too µch television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks

Average timespent watching TV

Less than1 hour

Between1 and 2 hours

More than2 hours

Less than 2 hours

90

85

130

More than 2 hours

655

32

8

Referring to the table, to test whether there is any relationship between average time spent watching TV and average time spent reading storybooks, the value of the measured test statistic is:    a. -12.59    b. 1.61    c. 481.49    d. 1,368.06
Q34. A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (Y) — measured in dollars per month — for services rendered to local companies. One independent variable used to predict service charge to a company is the company’s sales revenue (X) — measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model:
E(Y) = ß0 + ß1X
The results of the simple linear regression are provided below.
Y = -2,700+20X, syx = 65, two-tailed p value = 0.034 (for testing ß1)
Referring to Table 13-1, interpret the p value for testing whether ß1 exceeds 0.    a. There is sufficient evidence (at the α = 0.05) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).    b. There is insufficient evidence (at the α = 0.10) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).    c. Sales revenue (X) is a poor predictor of service charge (Y).    d. For every \$1 million increase in sales revenue, we expect a service charge to increase \$0.034.
Q35. A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.

Hispanic

Non-Hispanic

Seat belts worn

31

148

Seat belts not worn

283

330

Referring to the table, which test would be used to properly analyze the data in this experiment?     a. chi-square test for independence in a two-way contingency table.    b. chi-square test for equal proportions in a one-way table.     c. ANOVA F test for interaction in a 2 x 2 factorial design.    d. chi-square test for a 2 x 2 factorial design.
Q36. The Journal of Business Venturing reported on the activities of entrepreneurs during the organization creation process. As part of a designed study, a total of 71 entrepreneurs were interviewed and divided into 3 groups: those that were successful in founding a new firm (n1 = 34), those still actively trying to establish a firm (n2 = 21), and those who tried to start a new firm but eventually gave up (n3 = 16). The total number of activities undertaken (e.g., developed a business plan, sought funding, looked for facilities) by each group over a specified time period during organization creation was measured. The objective is to compare the mean number of activities of the 3 groups of entrepreneurs. Because of concerns over necessary assumption of the parametric analysis, it was decided to use a nonparametric analysis. Identify the nonparametric method that would be used to analyze the data.    a. Wilcoxon Rank Sums Test    b. Wilcoxon Signed Rank Test    c. Kruskal-Wallis Rank Test for Differences in Medians    d. One-way ANOVA F test
Q37. A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.

Size

Mean

Std Dev

Females

18

48,266.7

13,577.63

Males

12

55,000

11,741.29

Std Error = 4,764.82

Means Diff = -6,733.3

Z = -1.4528 2-tailed p value = 0.1463

T = -1.4221 2-tailed p value = 0.1574

Referring to the table, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. According to the test run, which of the following is an appropriate alternative hypothesis?    a. H1: μfemales > μmales    b. H1: μfemales < μmales    c. H1: μfemales ≠ μmales    d. H1: μfemales = μmales Q38. A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day’s transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.  Memory Location: 1 2 3 4 5 Number of Transactions: 82 100 74 92 102 Number of Reported Errors 11 12 6 9 10   The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ. Referring to the table, which test would be used to properly analyze the data in this experiment?    a. chi-square test for independence in a two-way contingency table     b. chi-square test for equal proportions in a one-way table     c. ANOVA F test for main treatment effect    d. Z test for the difference in two proportions Q39. If a test of hypothesis has a Type I error probability (α) of 0.01, we mean    a. if the null hypothesis is true, we don’t reject it 1% of the time.    b. if the null hypothesis is true, we reject it 1% of the time.    c. if the null hypothesis is false, we don’t reject it 1% of the time.    d. if the null hypothesis is false, we reject it 1% of the time. Q40. The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.  Hypothesized Difference 0Level of Significance 0.05Group 1Number of Successes 163Sample Size 227Group 2Number of Successes 154Sample Size 262Group 1 Proportion 0.718061674Group 2 Proportion 0.58778626Difference in Two Proportions 0.130275414Average Proportion 0.648261759Test Statistic 3.00875353Two-Tailed TestLower Critical Value -1.959961082Upper Critical Value 1.959961082p-Value 0.002623357 Referring to the table, if you want to test the claim that “Resort 1 (Group 1) has a higher proportion of satisfied guests compared to Resort 2 (Group 2),” the p-value of the test will be     a. 0.00262     b. 0.00262/2     c. 2*(0.00262)     d. 1 – (0.00262/2)

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