BA578 Final exam
FinalExam v There are 4 parts: Part A: True/ False (115) Part B: Answer the following questions (1621) Part C: Select the correct answer for the following questions (2260) Part D: Work Problem (6171) **All work must be shown step by step** v Two different ways to submit your answer sheet
v **Excel is not acceptable for this test v **Deadline:Monday, 4^{th} of Augest 2014 by noon v **All work must be shown step by step in order to receive credit

Part A: True or False (115)
____ ___ 1. The usual objective of regression analysis is to predict estimate the value of one variable when the value of another variable is known.
___ ____ 2. Correlation analysis is concerned with measuring the strength of the relationship between two variables.
___ ____ 3. In the least squares model, the explained sum of squares is always smaller than the regression sum of squares.
___ ___ 4. The sample correlation coefficient and the sample slope will always have the same sign.
___ ____ 5. An important relationship in regression analysis is = .
__ _____ 6. If zero is contained in the 95% confidence interval for b_{1}, we may reject H_{o}: b_{1} = 0 at the 0.05 level of significance.
____ ___ 7. If in a regression analysis the explained sum of squares is 75 and the unexplained sum of square is 25, r^{2} = 0.33.
___ ____ 8. In general, the smaller the dispersion of observed points about a fitted regression line, the larger the value of the coefficient of determination.
____ ___ 9. 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.
__ _____10.An alternative hypothesis (H_{a}) is a theory that contradicts the null hypothesis. The alternative hypothesis will be accepted when there is strong evidence leading us to reject the null hypothesis.
___ ____ 11. The pvalue of a test depends on the observed data, but the critical values of a test do not.
_____ _ 12. Other things being equal, decreasing ? increases ?.
__ _____ 13. The larger the pvalue associated with a test of hypothesis, the stronger the support for the null hypothesis.
_____ __ 14. 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.
___ ____ 15. When we reject a true null hypothesis, we commit a Type I error.
Part B:Answer the following questions (1621)
16. What is the Null Hypothesis? Explain.
17. What is the Alternative Hypothesis? Explain.
18. Explain how you decide what statement goes into the null hypothesis and what
statement go into the alternative hypothesis.
19. When should the ztest be used?
20. When should the ttest be used?
21. What is a critical value?
Part C: Multiple Choice (22–60)
___ ___ 22. The variable about which the investigator wishes to make predictions or estimates is called the ____.
a. dependent variable b. unit of association
c. independent variable d. discrete variable
___ __ 23. 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
___ ___ 24. In the equation y = b_{0} +b_{1}(x), b_{0} is the _____.
a. coefficient of determination b. slope of the regression line
c. y intercept of the regression line d. correlation coefficient
___ ___ 25. In the equation y = b_{0} + b_{1}(x), b_{1} is the _____.
a. coefficient of determination b. slope of the regression line
c. y intercept of the regression line d. correlation coefficient
____ __ 26. 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
___ ___ 27. 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
___ ___ 28. The quantity is called the _______________ sum of square.
a. least b. explained
c. total d. unexplained
______ 29. If, in the regression model, b_{1} = 0, we say there is _____________ linear relationship between X and Y.
a. an inverse b. a significant
c. a direct d. no
__ ____ 30. If, in the regression model, b_{1} is negative, we say there is _____________ linear relationship between X and Y.
a. an inverse b. a significant
c. a direct d. no
__ ____ 31. 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.
__ ____ 32. In simple linear regression analysis, if the correlation coefficient is equal to 1.0,
_________.
a. the slope is equal to 1.0
b. all the variability in the dependent variable is explained by the independent variable.
c. the y intercept is equal to 1.0
d. the relationship between the two variables can be described as a bivariable normal distribution.
__ 33. The following results were obtained from a simple linear regression analysis. Total
sum of square = 5.7640. Explained sum of squares = 5.5415. Unexplained sum of squares = 0.2225. The coefficient of determination is ____
a. 0.0402 b. 0.0386
c. 0.9805 d. 0.9614
___ ___ 34. The following results were obtained as part of a simple linear correlation analysis: Y = 97.98 – 4.33x regression sum of squares = 2680. 27. Error sum of squares = 125.40. Total sum of squares = 2805.67. The sample correlation coefficient is ____
a. 0.9774 b. 0.9553
c. 0.2114 d. 0.0447
___ ___ 35. The following equation describes the relationship between output and labor input at a sample of work stations in a manufacturing plant: = 2.35 + 2.20x. Suppose, for a selected work station, the labor input is 5. The predicted output is _____________.
a. 4.55 b. 2.35
c. 2.20 d. 13.35
___ 36. In regression and correlation analyses, the entity on which sets of measurements are taken is called the ______________.
a. dependent variable b. independent variable
c. variables d. discrete variable
_ ___ 37. Given: : = 10, : ? 10, n = 12, = 0.01, and the computed test statistic is
2.394, the p value for the test is ____________________
a. Between 0.02 and 0.01 b. between 0.025 and 0.01
c. between 0.05 and 0.02 d. none of the above
_ ____38. The _________ is the smallest level of significance at which can be rejected.
a. value of b. p value
c. probability of committing of Type I error d. value of 1 
……….39. We say that sample results are significant when ____________.
a. is not rejected
b. is rejected
c. is smaller than the p value
d. the computed value of the test statistic fall in the acceptance region
___40. You perform a hypothesis test about a population mean on the basis of the following
information: the sampled population is normally distributed, s = 100, n =25, = 225, =
0.05, : > 220. The critical value of the test statistic is __________.
a. 2.0639 b. 1.7081
c.1.7109 d. 1.96
___ ___41. You perform a hypothesis test about a population mean on the basis of the following
information: n = 50, = 100, = 0.05, s = 30, : < 110. The computed value of the test
statistic is __________.
a. 2.3570 b.1.645
c.2.3570 d.4.24264
___ ___42. We commit a Type I error if we ________ a true null hypothesis.
a. fail to reject b. reject
c. accept d. compute
____ _43. Given: : ? 100, the alternative hypothesis is _________ if the test is one sided
and the critical value is negative.
a. < 100 b. > 100
c. = 100 d. ? 100
___ ___44. If we reject a null hypothesis, we conclude that the alternative hypothesis
__________.
a. may be true b.is true
c. is not true d. may not be true
___ ____45. You perform a hypothesis test about a population mean on the basis of the following
information: The sample population is normally distributed with a variable of 100, n = 25,
= 225, = 0.05, : >220. The critical value of the test statistic is __________.
a.2.5 b. 1.645
c. 1.7109 d. 1.96
__ _____46. Given : ? 25, : > 25, n = 14, = 0.05, = 36, and = 30, the critical value
of the test statistic is __________.
a.1.9444 b. 1.7613
c. 1.7709 d. 2.1180
_______47. Given : ? 70, : > 70, n = 10, = 0.01, = 49, and = 78, the critical value
of the test statistic is __________.
a.3.6140 b. 2.7640
c. 3.2498 d. 2.8210
___ ____48. The purpose of hypothesis testing is to help one reach a conclusion about
___________ by examining the data contained in ___________.
a. a population; a sample
b. an experiment ; a computer printout
c. a population; an event
d. a group of subjects; a probability statement
___ ___49. The probability of rejecting a true null hypothesis is also referred to as the _______
for the test.
a. p value b. critical value
c. rejection region d. level of significance
___ ____50. A null hypothesis is rejected at the level of significance when the p value is
_________.
a. less than or equal to ?
b. exactly equal to ? only
c. greater than or equal to ?
d. greater than or equal to the critical value of the test statistic
___ ___51. The two kinds of statistical hypotheses are the null hypothesis and the
__________hypothesis.
a. accepted b. rejected
c. alternative d. null
__ ____52. The statement of what the investigator is trying to conclude is placed in the _____
hypothesis.
a. accepted b. rejected
c. alternative d. null
_______53. The _______ hypothesis is the hypothesis that is tested.
a. accepted b. rejected
c. alternative d. null
_______54. If the null hypothesis is rejected, we concluded that the _______ hypothesis is true.
a. accepted b. rejected
c. alternative d. null
_______55. If the null hypothesis is not rejected, we conclude that the ________ hypothesis may
be true.
a. accepted b. rejected
c. alternative d. null
_______56. The statistic that used as a decision maker in a hypothesistesting procedure is called the __________.
a. test statistic b. sample statistic
c. unbiased statistic d. relevant statistic
_______57. The rejection of a true null hypothesis is called the ______ error.
a. standard b. Type I
c. critical d. Type II
_______58. The quantity that gives the probability that a false null hypothesis will be rejected is
called the ________ of the test.
a. power b. probability of a Type II error
c. significance level d. probability of a Type I error
______59. 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.
b. It is computed from sample data.
c. Its critical value(s) is/are obtained from appropriate tables of its sampling distribution.
d. It serves as a decision maker.
_______60. Which of the following statements is not true when applied to the level significance?
a. It is always equal to the probability of committing a Type I error.
b. It should always be established prior to collecting and analyzing the data.
c. It is always larger than the p value.
d. Under the curve of the relevant sampling distribution, it is the area above the rejection
region.
Part D:Must show all your work step by step in order to receive the full credit; Excel is not allowed. (6171)
61.Use the following information from anormal population with mean ? = 52 and variance ?^{2}= 22.5 to calculate the following questions.
a) find P (X >55 )
b) find P
c) find P
62. A random sample from a population with mean and standard deviation produced the following sample information:
n =110 x = 699 s = 20.4
a) Find a 95% confidence interval for the mean ?. Interpret this interval.
b) Find a 99% confidence interval for the mean ?. Interpret this interval.
63. 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 ? = 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?
64. Consider the following hypothesis test.
H_{o}: ? = 15
H_{a:} ? ? 15
A sample of 50 gives a sample mean of 14.2 and sample standard deviation of 5.
a) At ? = 0.02, what is the rejection rule?
b) Compute the value of the test statistic z.
c) What is the pvalue?
d) What is your conclusion?
65. 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 variance of 4.
a) At ? = 0.05, what is the rejection rule?
Reject null if z < 1:645
b) Compute the value of the test statistic
c) What is the pvalue?
d) What is your conclusion?
66.Fill in the table and find the following answers:

Months on job (x) 
Monthly sales (y) thousands of dollars 


XY 






1 
0.8 




2 
2.4 




4 
7 




5 
3.7 




8 
11.3 




9 
12 




12 
15 



Total 










a) Find .
b) Find .
c) Write the estimated regression equation.
d) Interpret the estimated regression equation.
e) Calculate the coefficient of determination (R^{2}).
f) Interpret the coefficient of determination (R^{2}).
g) Calculate the adjusted coefficient of determination (Adjusted R^{2}).
67. A regression model relating x, number of sales persons at a branch office, to y, annual sales at the office ($1000s), has been developed. The computer output from a regression analysis of the data follows.
The regression equation is
= 80.0 + 50.0X
Predictor Coef Stdev tratio
Constant 80.0 11.333 7.06
X 50.0 5.482 9.12
Analysis of Variance
SOURCE DF SS MS
Regression 1 6828.6 6828.6
Error 28 2298.8 82.1
Total 29 9127.4
a) Write the estimated regression equation.
b) How many branch offices were involved in the 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.
68.The following regression equation was obtained using the five independent variables.
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 RSq = 99.4% RSq(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) 
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?
69. Computer output:

Coefficients 
Std. Error 
tStat 
Pvalue 
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 



S_{e} =12.86986 Rsq = 0.862263 Rsq(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 H_{a}: 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? Explain how this statistic and the statistic referred to in part (f) help you to determine how well the model fits the data.
i) Test the overall utility of the model. What does the pvalue of the test statistic tell you?
70. For the following ANOVA table are the results from treating 4 cultures with 6 observations for each culture. The enzymes are contained in test tubes with differing levels of enzymes applied.
a) Please fill in the blank.
Source of Variation 
df 
SS 
MS 
F 
Treatment 
180 

Error 
60 

Total 
b) What are the null and alternate hypotheses?
c) What is your decision rule, Use
d) Indicate your statistical decision.
e) Is there a difference among the means?
71.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 ?2value significant at 5% level of significance?
b) Write the conclusion for this question.

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Solution: BA578 Final exam