BA 578 FINAL EXAM SUMMER I 2016 | Complete Solution

                                                                                                                 Name: __________________________
                                                                       ID:      ______________________
Online Final Exam
Part A: Fill in the blank (1-26)
    The purpose of hypothesis testing is to aid the manager or researcher in reaching a (an) __________________ concerning a (an) _______________ by examining the data contained in a (an) _______________ from that ____________________.
    A hypothesis may be defined simply as __________________________________________.
    There are two statistical hypotheses. They are the _________________ hypothesis and the _________________ hypothesis.
    The statement of what the investigator is trying to conclude is usually placed in the _________________ hypothesis.
    The _____________ hypothesis is the hypothesis that is tested.
    If the null hypothesis is not rejected, we conclude that the alternative _________________.
    If the null hypothesis is not rejected, we conclude that the null hypothesis _____________.
    A Type I error occurs when the investigator _____________________________.
    A Type II error occurs when the investigator _____________________________ .
    The probability of committing a Type I error is designated by the symbol ____________, which is also called the ___________________.
    Values of the test statistic that separate the acceptance region from the rejection are called _________________ values.
    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 ______________________ .
    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.
    When one is testing H0: µ= µ0 on the basis of data from a sample of size n from a normally distributed population with a known variance of σ2 , the test statistic is ____________________________________________________.
    When one is testing H0: µ= µ0 on the basis of data from a sample of size n from a normally distributed population with a unknown variance, the test statistic is ___________________________________________________.
    The null hypothesis contains a statement of __________________________________.
    The statement  µ ≥  0 is an inappropriate statement for the ____________ hypothesis.
    The rejection region consists of those values of the ______________ that will cause rejection of the null hypothesis. 
    The null hypothesis and the alternative hypothesis are ____________ of each other.
    Given  ,  H0: µ= µ0, then Ha : ___________________________________ .
    Given H0: µ ≤ µ0, then Ha : ___________________________________ .
    Given H0: µ ≥ µ0, then Ha : ___________________________________ .
    A statement of what you wish to conclude goes in the ______________.
    A market analyst believes that more than 30% of the adults in a certain area regularly read a certain magazine.  The analyst wishes to conduct a hypothesis test to see whether this belief will be supported.  The appropriate statistical hypotheses are: __________________.
    Given: H0: µ ≥ 50;  Ha: µ < 50; α  = 0.05.  A simple random sample of size 64 is drawn from a non-normally distributed population.   X ̅= 45, s2 = 256.  The computed value of the test statistic is _________________, which is compared for significance with a value from the ____________________ distribution.
    Given: H0: µ= 100;  Ha: µ ≠ 100;   α = 0.03;  computed z = 2.25,  p = 0.0244.  The null hypothesis should reject because __________________________________________.
Part B: Use questions number 27-50 from page 9-54 to 9-57 to write your answer below (27-50). 
27             35             43     
28             36             44     
29             37             45     
30             38             46     
31             39             47     
32             40             48     
33             41             49     
34             42             50     
Part C: Please fill in the blank and circle your decision or answer the following questions (51-53).
    State whether you would reject or fail to reject the null hypothesis in each of the following cases (two-tailed): Make a decision.
    
P = 0.12 ; α=0.05    Decision
    Reject / Fail to reject
    
P = 0.001 ; α=0.01    Decision
    Reject / Fail to reject

    State whether H_0 should be accepted or rejected for α=0.05, given the following; F^*= computed F (circle your decision)
    
F^* = 2.34; df = 2 and 11    Decision
    Reject / Fail to reject
    
F^* = 4.29; df = 3 and 24    Decision
    Reject / Fail to reject

    Given the following, complete the ANOVA table and make the correct inference. Using F-value to make a decision.
Source    SS    df    MS    F
Treatments    ____    2    3.24    ____
Error    ____    17    ____     
Total    40.98    ____          

    ANSWER
a) What is the hypothesis being tested in this problem?    

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

c) Number of observations?    

Part D: Explain below (54-55)
    What does the constant term capture in the equation?

    What does the constant term capture in the equation?

Part E: Must show all your work step by step in order to receive the full credit; Excel is not allowed (56-65).
    Given the following probabilities, find Z0 and please draw the shading the area

    Show your work    Please draw graphs
a.    P(Z≤Z_0 )=0.0060
    

b.    P(-1.67≤〖Z≤Z〗_0 )=0.8844

c.    P(Z>Z_0 )=0.0455
=

d.    P(Z_0≤Z≤3.02)=0.0009

e.    P(Z>Z_0 )=0.7224

f.    P(Z_0≤〖Z≤Z〗_0 )=0.9876
    

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

a) 

    b)

c)

    d)

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

    b)

c)

    Work on problem number 15 (a-c) on page 7-67
a) 

    b)

c)

    Use problem number 12 on page 8-11  to answer the following questions (a-d)

a) Mean

    b) Variance
c) Standard deviation

    d) Find a 90% confidence interval for the mean μ.  Interpret this interval
    Please fill in the computer printout and answer the following questions (a-b).
Given that α=0.05
SUMMARY OUTPUT                
Regression Statistics                
Multiple R    0.9037                
R Square    ______                
Adjusted R Square    ______                
Standard Error    ______                
Observations    ______                
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    ______    ______    ______    ______
X1    0.7    ______    3.65563    0.03535    ______    ______    ______    ______

a) Predicting Y given that X=5; confidence interval α=0.05

    b) Estimating mean given that X=5; confidence interval α=0.05
    The following regression equation was obtained using the five independent variables.   
Given that α=0.05
          
 

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? 

    Work on problem 3 on page 10-28 (a-d)
a) 

    b)

c)

    d)

    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 α=0.05 
Program    1    2    3    4    5    6    Total
Number    5    8    10    12    12    13    60

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

    b) Write the conclusion for this question

    Work on problem 10 on page 15-10

    What is you hypothesis testing
 

    What is your χ^2?

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

d) Write the conclusion for this question.