STAT FINAL EXAM

_______ 16. An important relationship in regression analysis is = .

_______ 17. If in a regression analysis the explained sum of squares is 75 and the unexplained sum of square is 25, r2 = 0.33.

_______ 18. When small values of Y tend to be paired with small values of X, the relationship between X and Y is said to be inverse.

_______ 19. The probability that the test statistic will fall in the critical region, given that H0 is true, represents the probability of making a type II error.

_______ 20. When we reject a true null hypothesis, we commit a Type I error.

Part C: Answer the following questions (21-26)

21. What is the Null Hypothesis? Explain.

22. What is the Alternative Hypothesis? Explain.

23. Explain how you decide what statement goes into the null hypothesis and what statement go into the alternative hypothesis.

24. When should the z-test be used?

25. When should the t-test be used?

26. What is the definition of P-Value?

Part D: Must show all your work step by step in order to receive the full credit; Excel is not allowed. (27-46)

27. Work on problem number 9 (a-f) on page 7-47

28. Work on problem number 1 (a-e) on page 7-68

29. Work on problem number 2 (a-c) on page 7-68

30. Work on problem number 7 (a-e) on page 7-69

31. Work on problem number 16 (a-b) on page 8-12

;Given that

32. State whether you would reject or fail to reject the null hypothesis in each of the following cases (two-tailed):

a) P = 0.12 ;

b) P = 0.03 ;

c) P = 0.001 ;

d) P = 0.01 ;

33. Consider the following hypothesis test.

Ho: µ = 17

Ha: µ ≠ 17

A sample of 25 gives a sample mean of 14.2 and sample variation of 25.

a)	At α = 0.05, what is the rejection rule?	b)	Compute the value of the test statistic
c)	What is the p-value?	d)	What is your conclusion?

34. Consider the following hypothesis test.

Ho: μ = 15

Ha: μ ≠ 15

A sample of 50 gives a sample mean of 14.2 and sample variation of 25.

a)	At α = 0.05, what is the rejection rule?	b)	Compute the value of the test statistic
c)	What is the p-value?	d)	What is your conclusion?

35. Consider the following hypothesis test

Ho: µ ≥ 10

Ha: µ <10

A sample of 50 provides a sample mean of 9.46 and sample variation of 4.

a)	At α = 0.05, what is the rejection rule?	b)	Compute the value of the test statistic
c)	What is the p-value?	d)	What is your conclusion?

36. Fill in the table and find the following answers:

Months on job (x)	Monthly sales (y) thousands of dollars	X2	Y2	XY
1	0.80
2	2.40
4	7.00
5	3.70
8	11.30
9	12.00
12	15.00
41

a) Find

b) Find

c) Write the estimated regression equation

d) Interpret

e) Calculate the coefficient of determination

f) Interpret the coefficient of determination

37. Work on problem number 3 (a-d) on page 10-32

38. Please fill in the computer printout and answer the following questions.

Given that

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9037
R Square	______
Adjusted R Square	______
Standard Error	______
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	4.9	______	______	0.03535
Residual	3	1.1	______
Total	______	______

	Coefficients	Standard Error	t Stat	P-value	Lower95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.1	______	-0.15746	0.88488	-2.12112	1.92112	-2.12112	1.92112
X1	0.7	______	3.65563	0.03535	0.09061	1.30939	______	______

a)	What percent of the variation is explained by the regression equation?	b)	What is the standard error of regression?
c)	What is the critical value of the F-statistic?	d)	What sample size is used in the print out?

39. The following regression equation was obtained using the five independent variables.

Given that

a)	What percent of the variation is explained by the regression equation?	b)	What is the standard error of regression?
c)	What is the critical value of the F-statistic?	d)	What sample size is used in the print out?
e)	What is the variance of the slope coefficient of income?
f)	Conduct a global test of hypothesis to determine if any of the regression coefficients are not zero.
g)	Conduct a test of hypothesis on each of the independent variables. Would you consider eliminating outlets and bosses?
40. Please use the following computer printout to answer the following questions: Coefficients Std. Error t-Stat P-value Intercept 729.8665 169.25751 4.3121659 0.0010099 Price -10.887 3.4952397 -3.1148078 0.0089406 Advertising 0.0465 0.0176228 2.6386297 0.0216284 ANOVA df SS MS F Significance F Regression 2 12442.8 6221.4 37.56127994 0.00000683 Residual 12 1987.6 165.63333 Total 14 14430.4

Se =12.86986 R-sq = 0.862263 R-sq(adj) = 0.8393068

a) Write and interpret the multiple regression equation.

b) Does the model with Price and Advertising contribute to the prediction of Y? Use a 0.05 significance level.

c) Which independent variable appears to be the best predictor of sales? Explain.

d) What is the number of observations used in this study?

e) Assuming that the coefficient on Advertising has Ha: B1 > 0, what statistical decision should be made at 5% level.

f) What is the standard error of estimate? Can you use this statistic to assess the model’s fit? If so, how?

g) What is the coefficient of determination, and what does it tell you about the regression model?

h) What is the coefficient of determination, adjusted for degrees of freedom? What do this statistic and the statistic referred to in part (g) tell you about how well this model fits that data.

i) Test the overall utility of the model. What does the p-value of the test statistic tell you?

41. State whether should be accepted or rejected for , given the following;

a) = 2.34; df = 2 and 11

b) = 2.52; df = 4 and 20

c) = 4.29; df = 3 and 24

42. Given the following, complete the ANOVA table and make the correct inference.

Source	SS	df	MS	F
Treatments	____	2	3.24	____
Error	____	17	____
Total	40.98	____
		ANSWER
a)	In the above ANOVA table, is the factor significant at 5% level of significant?
b)	What is the number of observations?

43. Given the following, complete the ANOVA table and make the correct inference.

Source	SS	df	MS	F
Treatments	5	____	205.5	____
Error	____	637	____
Total	25	____
		ANSWER
a)	In the above ANOVA table, is the factor significant at 5% level of significant?
b)	What is the number of observations?

44. Given the following, complete the ANOVA table and make the correct inference.

Source	SS	df	MS	F
Treatments	____	3	____	____
Error	88.8	____	____
Total	435	19
		ANSWER
a)	In the above ANOVA table, is the factor significant at 5% level of significant?
b)	What is the number of observations?

45. A metropolitan bus system sampler’s rider counts on one of its express commuter routes for a week. Use the following data to establish whether the rider ship is evenly balanced by day of the week. Let

Day	Monday	Tuesday	Wednesday	Thursday	Friday
Rider Count	10	34	21	57	44

a) Is the χ2 value significant at 5% level of significance?

b) Write the conclusion for this question

46. A marketing research firm wished to study the relationship between wine consumption and whether a person likes to watch professional tennis on television. One hundred randomly selected people are asked whether they drink wine and whether they watch tennis. The following results are obtained:

	Watch Tennis	Do not Watch Tennis	Totals
Drink Wine	16	24	40
Do not Drink Wine	4	56	60
Totals	20	80	100

Test the hypothesis that whether people drink wine is independent of whether people watch tennis. Set α = 0.05

a) Is the χ2 value significant at 5% level of significant?

b) Write the conclusion for this question

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The regression equation is

sales = - 19.7 - 0.00063 outlets + 1.74 cars + 0.410 income + 2.04 age

- 0.034 bosses

Predictor Coef SE Coef T P

Constant -19.672 5.422 -3.63 0.022

outlets -0.000629 0.002638 -0.24 0.823

cars 1.7399 0.5530 3.15 0.035

income 0.40994 0.04385 9.35 0.001

age 2.0357 0.8779 2.32 0.081

bosses -0.0344 0.1880 -0.18 0.864

S = 1.507 R-Sq = 99.4% R-Sq(adj) = 98.7%

Analysis of Variance

Source DF SS MS F P

Regression 5 1593.81 318.76 140.36 0.000

Residual Error 4 9.08 2.27

Total 9 1602.89

(Minitab Software)

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