Project #19653 - MBA Quant Stats

 

PART A: True/False and Multiple Choice 

 

1.

A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest. 
 
a. True                                 

 

2.

Like the z distribution, the t distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it. 
 
b. False

 

3.            Another name for an explanatory variable is the dependent variable.

 

                b. False

 

 

4.            A goodness-of-fit test analyzes for two qualitative variables whereas a chi-square test of             a contingency table is for a single qualitative variable.

 

                b. False

 

5.            On the basis of sample information, we either "accept the null hypothesis" or "reject the             null hypothesis."

 

                b. False

 

6.

As a general guideline, we use the alternative hypothesis as a vehicle to establish something new, or contest the status quo, for which a corrective action may be required.
 
a. True                                 

 

 

7.

Two random samples are considered independent if the observations in the first sample are different from the observations of the second sample. 
 
a. True 

 

 

8.

 

 

What type of test for population means should be performed when examining a situation in which employees are first tested, then trained, and finally retested? 

 

A. 

A z test under independent sampling with known population variances

 

B. 

A t test under independent sampling with unknown but equal population variances

 

C. 

A t test under dependent sampling

 

D. 

A t test under independent sampling with unknown and unequal population variances

 

 

 

9.            A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she     test that claim?

 

 

                A.            A hypothesis test for 

 

                B.            A hypothesis test for 

 

                C.            A matched-pairs hypothesis test for μD

 

                D.            We are unable to conduct a hypothesis test since the samples would not be       independent.

 

10.

Which of the following set of hypotheses are used to test if the mean of the first population is smaller than the mean of the second population, using matched-pairs sampling? 
 

A. 



 

B. 



 

C. 



 

D. 

 

 

11. In regression, multicollinearity is considered problematic when two or more explanatory variables are: 
 

                A. 

not correlated.

 

                B. 

rarely correlated.

 

                C. 

highly correlated.

 

                D. 

moderately correlated.

 

12.

The number of dummy variables representing a qualitative variable should be: 
 

A. 

one less than the number of categories of the variable.

 

B. 

two less than the number of categories of the variable.

 

C. 

the same number as the number of categories of the variable.

 

D. 

None of the Answers.

 

 

13.

Which of the following variables is not qualitative? 
 

A. 

Gender of a person

 

B. 

Religious affiliation

 

C. 

Number of dependents claimed on a tax return

 

D. 

Student's status (freshman, sophomore, etc.)

 

 

 

14.  The null hypothesis in a hypothesis test refers to _____________. 
 

A. 

the desired outcome

 

B. 

the default state of nature

 

C. 

the altered state of nature

 

D. 

the desired state of nature

 

 

 

 

 

15.

 

 

 

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies that are born out of wedlock is increasing. When testing the two hypotheses, H0: p ≤ 0.50 and HA: p > 0.50, p stands for _____________. 
 

A. 

the current proportion of babies born out of wedlock

 

B. 

the mean number of babies born out of wedlock

 

C. 

the number of babies born out of wedlock

 

D. 

the general belief that the proportion of babies born out of wedlock is no more than 0.50

 

 

16.

 

Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim. 
 

A. 

 and

 

B. 

 and

 

C. 

 and

 

D. 

 and

 

       

 

 

17.

What is the purpose of calculating a confidence interval? 
 

A. 

To provide a range of values that has a certain large probability of containing the sample statistic of interest

 

B. 

To provide a range of values that, with a certain measure of confidence, contains the sample statistic of interest

 

C. 

To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest

 

D. 

To provide a range of values that has a certain large probability of containing the population parameter of interest

 

 

18.

What is the most typical form of a calculated confidence interval? 
 

A. 

Point estimate ± Standard error

 

B. 

Point estimate ± Margin of error

 

C. 

Population parameter ± Standard error

 

D. 

Population parameter ± Margin of error

 

 

 

 

19.

The accompanying table shows the regression results when estimating        At the 5% significance level, which explanatory variable(s) is(are) individually significant?

  

   

A. 

Only x1

 

B. 

Only x3

 

C. 

x1 and x2

 

D. 

x2 and x3

 

 

20.

The accompanying table shows the regression results when estimating   Is x significantly related to y at the 5% significance level?

   

A. 

Yes, since the p-value of 0.0745 is greater than 0.05.

 

B. 

No, since the p-value of 0.0745 is greater than 0.05.

 

C. 

Yes, since the slope coefficient of 1.417 is less than the test statistic of 2.25.

 

D. 

No, since the slope coefficient of 1.417 is less than the test statistic of 2.25.

 

 

21.

Consider the following simple linear regression model:   When determining whether there is a positive linear relationship between x and y, the alternative hypothesis takes the form: 
 

A. 

 

B. 

 

C. 

 

D. 

 

 

 

22.

Using the same data set, four models are estimated using the same response variable; however, the number of explanatory variables differs. Which model provides the best fit?

    

A. 

Model 1

 

B. 

Model 2

 

C. 

Model 3

 

D. 

Model 4

 

 

23.

The coefficient of determination R2 is _________. 
 

A. 

sometimes negative

 

B. 

always lower than adjusted R2

 

C. 

usually higher than adjusted R2

 

D. 

always equal to adjusted R2

 

 

 

24.

The R2 of a multiple regression of y  on x1 and x2 measures the: 
 

A. 

percent variability of y that is explained by the variability of x1.

 

B. 

percent variability of y that is explained by the variability of x2.

 

C. 

statistical significance of the coefficients in the regression equation.

 

D. 

percent variability of y that is explained by the variability of x1 and x2.

 

 

 

25. Consider the sample regression equation      When x1 increases 1 unit and x2 increases 2 units, while x3 and x4 remain unchanged, what change would you expect in the predicted y
 

A. 

Decrease by 2

 

B. 

Decrease by 4

 

C. 

Decrease by 7

 

D. 

No change in predicted y

 

 

 

 

 

 

 

 

 

 


 

PART B: Problems

 

For the next 5 questions, refer to printout B1 below. The dependent variable is Risk of a stroke measured as the probability of having a stroke in the next 10 years.  The independent variables are Age, Blood Pressure, and the qualitative variable Smoker. Variable Smoker is coded 0 if subject does not smoke, and coded 1 if the subject smokes. In the analysis, use a significance level of 5% 

 

Printout B1

 

Regression Statistics

 

 

 

 

 

 

Multiple R

0.79416

 

 

 

 

 

R 2

0.63069

 

 

 

 

 

Adjusted R2

0.56145

 

 

 

 

 

Standard Error

9.83533

 

 

 

 

 

Observations

20.00000

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

 

df

SS

MS

F

Significance F

 

Regression

3

2643.20902

881.06967

9.10819

0.00095

 

Residual

16

1547.74098

96.73381

 

 

 

Total

19

4190.95000

 

 

 

 

 

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

-25.11270

19.53852

-1.28529

0.21698

-66.53251

16.30711

Age

0.69721

0.25871

2.69498

0.01593

0.14878

1.24564

BloodPressure

-0.02376

0.07458

-0.31863

0.75413

-0.18187

0.13434

Smoker

14.74974

4.95024

2.97960

0.00885

4.25570

25.24377

 

1.  Predict the Risk of a stroke over the next 10 years for Art Speen, a 68-year-old smoker who has blood pressure of 155 mmHg, and the 95% prediction interval.

 

2.  How much of the variation in the risk of a patient will have a heart attack in the next 10 years is explained by the model?

 

3. Is the estimated regression model significant?

 

4.a) Is smoking a significant factor in the risk of a stroke?

4.b) Explain the numerical meaning of the regression coefficient for the Smoker variable.

 

5.  Does the model have a practical significance?

 

6. Consider the following table comparing 3 flat screen TVs according to consumers’ ratings (use 4 decimal points for precision where required; higher rating points means higher consumer’s satisfaction with the product):

 

Table of Product Ratings

Plasma

LCD

ES

15

16

8

18

17

7

17

21

10

19

16

15

19

19

14

20

17

14

 

Compute the ANOVA table and test whether there is a difference in ratings among the 3 product types.  Write the hypothesis and discuss your results.  In the analysis, use a significance level of 5%.

 

 

7.  The US Energy Information Administration releases figures in their publication, Monthly Energy review, about the cost of various fuels and electricity.  Shown here are the figures for five different items over a 12 year period. Use the data to estimate a ‘preferred’ regression model to predict the cost of residential electricity from the cost of natural gas, residual fuel oil, unleaded regular gasoline, and type of residential unit.  Discuss the output of your model (practical utility and statistical significance) assuming a 5% significance level and an initial hypothesized model given by

 

E(Electricity) = B0 + B1(Nat. Gas) + B2(Fuel oil) + B3(Gasoline) + B4 (Building Type),  where:

 

Residential Type = 0 if one story floor plan;

Residential Type = 1 if multi story plan.

 

Electricity

($/kWh)

Natural Gas ($/1000ft3)

Fuel Oil ($/gal)

Gasoline ($/gal)

Building Type (1 or 0)

2.54

1.29

1.21

2.39

1

3.51

1.71

1.31

2.57

1

4.64

2.98

1.44

2.86

0

5.36

3.68

1.61

3.19

0

6.2

4.29

1.76

3.31

0

6.86

5.17

1.68

3.22

0

7.18

6.06

1.65

3.16

1

7.54

6.12

1.69

3.13

1

7.79

6.12

1.61

3.12

1

7.41

5.83

1.34

2.86

1

7.41

5.54

1.42

2.9

0

7.49

4.49

1.33

2.9

1

 

 

8. Given the following registered voter table:

 

Do you support amendment #234?

Democrats

Republicans

Yes

525

390

No

548

410

 

Is there significant evidence of a difference between the proportion of democrats and republicans who support Amendment #234? That is, state the hypothesis, the 3-part conclusion, and appropriate statistics. (Use a significance level of 10%).

 

 

9. When estimating a multiple regression model based on 30 observations, the following results were obtained:

 

 

 

a. Specify the hypotheses to determine whether x1 is linearly related to y. At the 5% significance level, use the p-value approach to complete the test. Are x1 and y linearly related?

 


b. Construct the 95% confidence interval for β2. Using this confidence interval, is x2 significant in explaining y? Explain.



 

 

 

10. A large city installed LED street lights, in part, to help reduce crime in particular areas. The city collected the number of property crimes along 9 randomly selected streets in the month before and after the LED light installation, and claims that crime has been reduced. The crime data are shown next.

  

a. Specify the competing hypotheses to test the city's claim.
b. Calculate the value of the relevant test statistic, and find the critical value at the 5% significance level.
c. Does the evidence support the city's claim at the 5% significance level? 
 

Subject Mathematics
Due By (Pacific Time) 12/11/2013 02:05 pm
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