Name: _______________

                                                                             ID:      _______________

Online Final Exam

 

Part A: Fill in the blank (1-5)

1.      The following is a general statement of a decision rule: If, when the null hypothesis is true, the probability of obtaining a value of the test statistic as____________ as or more ___________ than that actually obtained is less than or equal to, the null hypothesis is_______________.  Otherwise, the null hypothesis is ______________.

2.      The probability of obtaining a value of the test statistic as extreme as or more extreme than that actually obtained, given that the tested null hypothesis is true, is called ____________ for the ________________test.

3.      Given: H₀: µ ≥ 50; H_a: µ < 50; α = 0.05.  A simple random sample of size 64 is drawn from a non-normally distributed population.   = 45, s² = 256.  The computed value of the test statistic is _________________, which is compared for significance with a value from the ____________________ distribution.

4.      Given H₀: µ ≤ µ₀, then H_a: _______________________.

5.      Given H₀: µ ≥ µ₀, then H_a: _______________________.

 

Part B: True or False (6-15)

________ 6. 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.

 

________7. If zero is contained in the 95% confidence interval for b, we may reject H_o: b = 0 at the 0.05 level of significance.

 

________8. 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.

 

________9. The usual objective of regression analysis is to predict estimate the value of one variable when the value of another variable is known.

 

________10. In the least squares model, the explained sum of squares is always smaller than the regression sum of squares.

 

________11. If in a regression analysis the explained sum of squares is 75 and the unexplained sum of square is 25, r² = 0.33.

 

________12. Correlation analysis is concerned with measuring the strength of the relationship between two variables.

 

________13. In general, the smaller the dispersion of observed points about a fitted regression line, the larger the value of the coefficient of determination.

 

________14. The sample correlation coefficient and the sample slope will always have the same sign.

 

________15. The p-value of a test depends on the observed data, but the critical valuesof a test do not.                                                                                

 

Part C: Short Answer (16-22)

16.  What is the p-value?

 

 

 

 

17.  What is the important of having a critical value?

 

 

18.  What is a null hypothesis? And what is an alternative hypothesis?

 

 

 

 

19.  Explain how to decide what statement goes into the null hypothesis and what statement goes into the alternative hypothesis?

 

 

 

 

20.  Show 3 ways how to calculate coefficient determination.

 

 

 

 

21.  When to use Z-test?

 

 

 

22.  When to use T-test?

 

 

Part D: Multiple Choice (23–32)

______ 23. The statistic that is used as a decision maker in a hypothesis-testing procedure is called the ______________.

a.   test statistic                                                     b.         sample statistic

c.   unbiased statistic                                             d.         relevant statistic

 

______ 24. If two variables are not related, we know that ________________.

      a. their correlation coefficient is equal to zero.

      b. the variability in one of them cannot be explained by the other.

      c. the slope of the regression line for the two variables is equal to zero.

      d. all of the above statements are true.

 

______ 25. Which of the following statements is not necessarily true when applied to a test statistic?

a.   It is normally distributed with a mean of 0 and a variance of 1.

1. It is computed from sample data
2. Its critical value(s) is/are obtained from appropriate tables of its sampling distribution
3. It serves as a decision maker.

 

______ 26. In regression and correlation analysis, the entity on which sets of measurements are taken is called the ______________.

a. dependent variable                              b. independent variable

            c. variables                                          d. discrete variable

 

______  27. You perform a hypothesis test about a population mean on the basis of the following information: The sampled population is normally distributed with a variance of 100, n= 25,  = 225, α = 0.05, H_a: µ > 220.  The critical value of the test statistic is ________

a. 2.5                                                        b. 1.645

c. 1.7109                                                  d. 1.96

 

______ 28. A null hypothesis is rejected at the level of significance when the p value is

a.   Less than or equal to α 

b.   Exactly equal to α only

1. Greater than or equal to α
2. Greater than or equal to the critical value of the test statistic

 

______ 29. In regression analysis, the quantity that gives the amount by which Y changes for a unit change in X is called the _____.

      a. coefficient of determination                       b. slope of the regression line

      c. Y intercept of the regression line               d. correlation coefficient

 

______ 30. When testing a hypothesis, if you fail to reject Ho, which of the following is not true?

a.          The significance level for the test remains the same.

b.         A Type II error may have been committed.

c.          The p value is greater than α.

d.         The p value is less than α.     

 

______31. In regression and correlation analysis, the measure whose values are restricted to the range -1 to +1, inclusive, is the____.

      a. coefficient of determination                       b. slope of the regression line

      c. y intercept of the regression line                d. correlation coefficient

 

______ 32. In regression and correlation analysis, the measure whose values are restricted to the range 0 to 1, inclusive, is the _____.

      a. coefficient of determination   b. slope of the regression line

      c. Y intercept of the regression line               d. correlation coefficient

Part E: Must show all your work step by step in order to receive the full credit; Excel is not allowed. (33-51)

33.  Given the following probabilities, find Z₀ and please draw the shading the area

 

	Show your work	Please draw graph
a)	P
b)	P
c)	P
d)	P
e)	P
f)	P

 

 

34.  Work on problem number 28 (a-d) on page 7-26

 

a)	b)
c)	d)

 

35.  Work on problem number 13 (a-c) on page 7-48

 

a)	b)
c)

36.  Work on problem number 15 (a-c) on page 7-70

a)	b)
c)

 

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

;Given that

 

a)

b)

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

a)      P = 0.15 ;

 

 

 

 

b)      P = 0.003 ;

 

 

 

 

c)      P = 0.11 ;

 

 

 

 

 

d)     P = 0.001 ;

 

 

 

 

 

39.  Consider the following hypothesis test.

 

H_o: µ = 17

      H_a: µ ≠ 17

 

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

 

 

40.  Consider the following hypothesis test.

 

                                    H_o:   μ = 15

                                    H_a:   μ ≠ 15     

 

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

 

 

 

41.  Consider the following hypothesis test

 

H_o: µ ≥ 10

H_a: µ < 10

 

A sample of 50 provides a sample mean of 9.46 and sample standard deviationof 2.

 

 

42.  Use problem number 1 on page 10-24 toanswer the following questions (a-h)

 

a)      Find	b)      Find
c)      Write the equation	e)      Find
f)       Find SST	g)      Find
g)Construct the 95% confidence interval for the mean of y when x = 7	h) Construct the 95% confidence interval for the individual value when x = 9

 

43.  Use problem number 3 on page 10-32 to fill in the table and find the answers for the following questions (a-d):

           

 

a)Write the estimated regression equation	b)  How many branch offices were involved in this study
c)Compute the F statistic and test the significance of the relationship at a .05 level of significance.	d)  Predict the annual sales at the Memphis branch office. This branch has 12 sales persons.

 

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

 

SUMMARY OUTPUT		Given that
Regression Statistics
Multiple R	0.11992852
R Square	_________
Adjusted R Square	_________
Standard Error	_________
Observations	_________
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6.0538	6.0538	_____________	0.7414
Residual	8	414.8472	_____________
Total	_____________	420.9010

 

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-3.9330	__________	-0.6656	0.5244	__________	9.6930	-17.5589	__________
Price	0.2306	__________	0.3417	0.7414	__________	1.7867	-1.3256	__________

 

 

 

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

Given that

 

 

 

46.  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

 

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

 

 

 

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

 

 

 

 

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

 

 

 

 

 

50.  An ad agency asks each member of a random sample of 60 viewers to indicate which of six television programs he or she prefers.Let

 

51.  A market research firm wishes to know whether they can conclude that, for adults in a certain city, the make of car driven is associated with the driver’s area of residence. A random sample of 500 adult drivers is in interviewed to determine what make of car they drive and in what area of the city they live. Let