Final Exam | Complete Solution

Final Exam
 There are 4 parts:
Part A: Fill in the blank (1-26)
Part B: Write your answers (27-50)
Part C: Fill in the blank and circle your answers (51-53)
Part D: Explaination (54-55)
Part E: Work Problem (56-65) **This part all work must be shown step by step**
 Two different ways to submit your answer sheet
1. Scan your answer sheet and place it in ONE FILE at drop-box. (preferable)
2. Use MS-Word and place it in a drop-box.
 **Excel is not acceptable for this test
 **Deadline: Sunday, 3rd of July 2016 by 11:59 PM (CST)
 **Part E: All work must be shown step by step in order to receive full credit

Part A: Fill in the blank (1-26)
1) 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 ____________________.
2) A hypothesis may be defined simply as __________________________________________.
3) There are two statistical hypotheses. They are the _________________ hypothesis and the
_________________ hypothesis.
4) The statement of what the investigator is trying to conclude is usually placed in the
_________________ hypothesis.
5) The _____________ hypothesis is the hypothesis that is tested.
6) If the null hypothesis is not rejected, we conclude that the alternative _________________.
7) If the null hypothesis is not rejected, we conclude that the null hypothesis _____________.
8) A Type I error occurs when the investigator _____________________________.
9) A Type II error occurs when the investigator _____________________________ .
10) The probability of committing a Type I error is designated by the symbol ____________, which is
also called the ___________________.
11) Values of the test statistic that separate the acceptance region from the rejection are called
_________________ values.
12) 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 ______________________ .
13) 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.
14) 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
____________________________________________________.
15) 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
___________________________________________________.
16) The null hypothesis contains a statement of __________________________________.
17) The statement µ ≥ 0 is an inappropriate statement for the ____________ hypothesis.
18) The rejection region consists of those values of the ______________ that will cause rejection of the
null hypothesis.
19) The null hypothesis and the alternative hypothesis are ____________ of each other.
20) Given , H0: µ= µ0, then Ha : ___________________________________ .
21) Given H0: µ ≤ µ0, then Ha : ___________________________________ .
22) Given H0: µ ≥ µ0, then Ha : ___________________________________ .
23) A statement of what you wish to conclude goes in the ______________.
24) 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: __________________.
25) Given: H0: µ ≥ 50; Ha: µ < 50; α = 0.05. A simple random sample of size 64 is drawn from a nonnormally
distributed population. 𝑋̅= 45, s2
= 256. The computed value of the test statistic is
_________________, which is compared for significance with a value from the
____________________ distribution.
26) 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).
51. State whether you would reject or fail to reject the null hypothesis in each of the following cases
(two-tailed): Make a decision.
a)
P = 0.12 ; 𝛼 = 0.05 Decision
Reject / Fail to reject
b)
P = 0.001 ; 𝛼 = 0.01 Decision
Reject / Fail to reject
52. State whether H0 should be accepted or rejected for α = 0.05, given the following; F
∗ =
computed F (circle your decision)
a)
𝐹
∗ = 2.34; df = 2 and 11 Decision
Reject / Fail to reject
b)
𝐹
∗ = 4.29; df = 3 and 24 Decision
Reject / Fail to reject
53. 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)
54. What does the constant term capture in the equation?
55. What does the error 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).
56. Given the following probabilities, find Z0 and please draw the shading the area
Show your work Please draw graphs
a. P(𝑍 ≤ 𝑍0
) = 0.0060
b. P(−1.67 ≤ 𝑍 ≤ 𝑍0
) = 0.8844
c. P(𝑍 > 𝑍0
) = 0.0455
=
57.
a) b)
c) d)
d. P(𝑍0 ≤ 𝑍 ≤ 3.02) = 0.0009
e. P(𝑍 > 𝑍0
) = 0.7224
f. P(𝑍0 ≤ 𝑍 ≤ 𝑍0
) = 0.9876
58.
a) b)
c)
59.
a) b)
c)
60.
a) Mean b) Variance
c) Standard deviation d) Find a 90% confidence interval for the mean μ.
Interpret this interval
61. 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
62. 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?
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)
63.
a) b)
c) d)
64. 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
a) What is you hypothesis testing
b) What is your 𝜒
2
?
c) Is the χ2 value significant at the 5 % level of significance?
d) Write the conclusion for this question.