Name: _______________
ID: _______________
Online Final Exam
Part A: Fill in the blank (15)
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: H_{0}: µ 50; H_{a}: µ < 50; α = 0.05. A simple random sample of size 64 is drawn from a nonnormally distributed population. = 45, s^{2} = 256. The computed value of the test statistic is _________________, which is compared for significance with a value from the ____________________ distribution.
4.Given H_{0}: µ ≤ µ_{0}, then H_{a}: _______________________.
5.Given H_{0}: µ µ_{0}, then H_{a}: _______________________.
Part B: True or False (615)
________ 6. The probability that the test statistic will fall in the critical region, given that H_{0} 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, r^{2} = 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 pvalue of a test depends on the observed data, but the critical valuesof a test do not.
Part C: Short Answer (1622)
 What is the pvalue?
 What is the important of having a critical value?
 What is a null hypothesis? And what is an alternative hypothesis?
 Explain how to decide what statement goes into the null hypothesis and what statement goes into the alternative hypothesis?
 Show 3 ways how to calculate coefficient determination.
 When to use Ztest?
 When to use Ttest?
Part D: Multiple Choice (23–32)
______ 23. The statistic that is used as a decision maker in a hypothesistesting 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.
 It is computed from sample data
 Its critical value(s) is/are obtained from appropriate tables of its sampling distribution
 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
 Greater than or equal to α
 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. (3351)
33.Given the following probabilities, find Z_{0} 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 (ad) on page 726
a)

b) 
c)

d) 
35.Work on problem number 13 (ac) on page 748
a)

b) 
c)

36.Work on problem number 15 (ac) on page 770
a)

b) 
c)

37.Work on problem number 16 (ab) on page 812
;Given that
a)

b) 
38.State whether you would reject or fail to reject the null hypothesis in each of the following cases (twotailed):
 P = 0.15 ;
 P = 0.003 ;
 P = 0.11 ;
 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.
a) 
At α = 0.05, what is the rejection rule? 
b) 
Compute the value of the test statistic 
c) 
What is the pvalue? 
d) 
What is your conclusion? 

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.
a) 
At α = 0.05, what is the rejection rule? 
b) 
Compute the value of the test statistic 


c) 
What is the pvalue? 
d) 
What is your conclusion? 

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.
a) 
At α = 0.05, what is the rejection rule? 
b) 
Compute the value of the test statistic 
c) 
What is the pvalue? 
d) 
What is your conclusion? 
42.Use problem number 1 on page 1024 toanswer the following questions (ah)






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 1032 to fill in the table and find the answers for the following questions (ad):




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 
Pvalue 
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 
__________ 
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 Fstatistic? 
d) 
What sample size is used in the print out? 

45.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 Fstatistic? 
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? 
46.State whether should be accepted or rejected for , given the following;
a) = 2.34; df = 2 and 11
Ftable value 
Decision 


b) = 2.52; df = 4 and 20
Ftable value 
Decision 


c) = 4.29; df = 3 and 24
Ftable value 
Decision 


 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? 


 Given the following, complete the ANOVA table and make the correct inference.
Source 
SS 
df 
MS 
F 


Treatments 
____ 
2 
24.9 
____ 


Error 
22.9 
____ 
____ 



Total 
____ 
29 




ANSWER 

a) 
In the above ANOVA table, is the factor significant at 5% level of significant? 


b) 
What is the number of observations? 


 Given the following, complete the ANOVA table and make the correct inference.
Source 
SS 
df 
MS 
F 


Treatments 
____ 
3 
____ 
____ 


Error 
1156.56 
____ 
____ 



Total 
2202 
23 




ANSWER 

a) 
In the above ANOVA table, is the factor significant at 5% level of significant? 


b) 
What is the number of observations? 


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
Program 
1 
2 
3 
4 
5 
6 
Total 
Number 
5 
8 
10 
12 
12 
13 
60 


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
Area of residence 
Make of automobile 

A 
B 
C 
Total 

1 
52 
64 
24 
140 
2 
60 
59 
52 
171 
3 
50 
65 
74 
189 
Total 
162 
188 
150 
500 


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