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.

2. 
Like the z distribution, the t distribution is symmetric around 0, bellshaped, and with tails that approach the horizontal axis and

3. Another name for an explanatory variable is the dependent variable.
b. False
4. A goodnessoffit test analyzes for two qualitative variables whereas a chisquare 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.

7. 
Two random samples are considered independent if the observations in the first sample are different from the observations of the second sample.

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?

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 matchedpairs 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 matchedpairs sampling?

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:

13. 
Which of the following variables is not qualitative?

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, H_{0}: p ≤ 0.50 and H_{A}: p > 0.50, p stands for _____________.


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.


17. 
What is the purpose of calculating a confidence interval?


18. 
What is the most typical form of a calculated confidence interval?

19. 
The accompanying table shows the regression results when estimating At the 5% significance level, which explanatory variable(s) is(are) individually significant?

20. 
The accompanying table shows the regression results when estimating Is x significantly related to y at the 5% significance level?

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:

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?

23. 
The coefficient of determination R^{2} is _________.

24. 
The R^{2} of a multiple regression of y on x_{1} and x_{2} measures the:

25. Consider the sample regression equation When x_{1} increases 1 unit and x_{2} increases 2 units, while x_{3} and x_{4} 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 R^{2} 
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 
Pvalue 
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 68yearold 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 ($/kWh) 
Natural Gas ($/1000ft^{3}) 
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 3part 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 x_{1} is linearly related to y. At the 5% significance level, use the pvalue approach to complete the test. Are x_{1} and y linearly related?
b. Construct the 95% confidence interval for β_{2}. Using this confidence interval, is x_{2} 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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