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##### BA578 Final exam 2014

FinalExam
v There are four components:
Half A: True/ False (1-15)
Half B: Reply the next questions
(16-21)
Half C: Choose the proper reply for
the next questions (22-60)
Half D: Work Downside (61-71) **All
work have to be proven step-by-step**
v Two other ways to submit your reply sheet
Scan
your reply sheet and place it inONE FILEat
drop-box. (preferable)Use
MS-Phrase and place it in a drop-box.
v **Excel is just not acceptable for this check
v **Deadline:Monday, 4th of
Augest 2014 by midday
v **All work
have to be proven step-by-step to be able to obtain credit score
On-line Ultimate Examination
Half A:
True or False (1-15)
____ ___ 1. The standard
goal of regression evaluation is to foretell estimate the worth of 1
variable when the worth of one other variable is understood.
___ ____ 2. Correlation
evaluation is worried with measuring the power of the connection between
two variables.
___ ____ three. Within the least
squares mannequin, the defined sum of squares is all the time smaller than the
regression sum of squares.
___ ___ four. The pattern
correlation coefficient and the pattern slope will all the time have the identical signal.
___ ____ 5. An essential
relationship in regression evaluation is
=
.
__ _____ 6. If zero is
contained within the 95% confidence interval for b1, we could reject Ho:
b1 = Zero on the Zero.05 stage of significance.
____ ___ 7. If in a regression
evaluation the defined sum of squares is 75 and the unexplained sum of sq.
is 25, r2 = Zero.33.
___ ____ eight. On the whole, the
smaller the dispersion of noticed factors a few fitted regression line, the
bigger the worth of the coefficient of dedication.
____ ___ 9. When small
values of Y are usually paired with small values of X, the connection between
X and Y is alleged to be inverse.
__ _____10.An alternate speculation (Ha) is a principle
that contradicts the null speculation. The choice speculation might be
accepted when there may be robust proof main us to reject the null
speculation.
___ ____ 11. The p-value of
a check depends upon the noticed information, however the vital values of a check do
not.
_____ _ 12. Different issues
being equal, reducing ? will increase ?.
__ _____ 13. The bigger the
p-value related to a check of speculation, the stronger the help for the
null speculation.
_____ __ 14. The
likelihood that the check statistic will fall within the vital area, given
that H0 is true, represents the likelihood of creating a kind II
error.
___ ____ 15. After we reject
a real null speculation, we commit a Sort I error.
Half B:Reply the next questions (16-21)
16. What's the Null
Speculation? Clarify.
17. What's the
Different Speculation? Clarify.
18. Clarify the way you resolve
what assertion goes into the null speculation and what
assertion go into the choice
speculation.
19. When ought to the z-test
be used?
20. When ought to the t-test
be used?
21. What's a vital
worth?
Half C: A number of Alternative
(22â60)
___ ___ 22. The variable
about which the investigator needs to make predictions or estimates is named
the ____.
a. dependent variable b. unit of
affiliation
c. impartial variable d. discrete
variable
___ __ 23. In regression
evaluation, the amount that provides the quantity by which Y modifications for a unit
change in X is named the _____.
a. coefficient of dedication b. slope of the
regression line
c. Y intercept of the regression line d. correlation coefficient
___ ___ 24. Within the equation
y = b0 +b1(x), b0 is the _____.
a. coefficient of dedication b. slope of the
regression line
c. y intercept of the regression line d. correlation coefficient
___ ___ 25. Within the equation
y = b0 + b1(x), b1 is the _____.
a. coefficient of dedication b. slope of the
regression line
c. y intercept of the regression line d. correlation coefficient
____ __ 26. In regression
and correlation evaluation, the measure whose values are restricted to the vary
Zero to 1, inclusive, is the _____.
a. coefficient of dedication b. slope of the
regression line
c. y intercept of the regression line d. correlation coefficient
___ ___ 27. In regression
and correlation evaluation, the measure whose values are restricted to the vary
-1 to +1, inclusive, is the
a. coefficient of dedication b. slope of the
regression line
c. y intercept of the regression line d. correlation coefficient
___ ___ 28. The amount
is named the _______________ sum of sq..
a. least b.
defined
c. complete d. unexplained
______ 29. If, within the
regression mannequin, b1 = Zero, we are saying there may be _____________ linear
relationship between X and Y.
a. an inverse b. a big
c. a direct d. no
__ ____ 30. If, within the
regression mannequin, b1 is unfavorable, we are saying there may be _____________
linear relationship between X and Y.
a. an inverse
b. a big
c. a direct
d. no
__ ____ 31. If two
variables aren't associated, we all know that ________________.
a. their correlation coefficient is the same as zero.
b. the variability in considered one of them can't be defined by the
different.
c. the slope of the regression line for the 2 variables is
equal to zero.
d. the entire above statements are true.
__ ____ 32. In easy
linear regression evaluation, if the correlation coefficient is the same as 1.Zero,
_________.
a. the slope is the same as 1.Zero
b. all of the variability within the dependent variable is defined
by the impartial variable.
c. the y intercept is the same as 1.Zero
d. the connection between the 2 variables might be described
as a bivariable regular distribution.
__ 33. The next
outcomes had been obtained from a easy linear regression evaluation. Complete
sum of sq. = 5.7640. Defined sum of
squares = 5.5415. Unexplained sum of squares = Zero.2225. The coefficient of
dedication is ____
a. Zero.0402
b. Zero.0386
c. Zero.9805
d. Zero.9614
___ ___ 34. The next
outcomes had been obtained as a part of a easy linear correlation evaluation: Y =
97.98 â four.33x regression sum of squares = 2680. 27. Error sum of squares =
125.40. Complete sum of squares = 2805.67. The pattern correlation coefficient is
____
a. -Zero.9774 b. Zero.9553
c. Zero.2114
d. Zero.0447
___ ___ 35. The next
equation describes the connection between output and labor enter at a pattern
of labor stations in a producing plant:
= 2.35 + 2.20x.
Suppose, for a specific work station, the labor enter is 5. The anticipated
output is _____________.
a. four.55
b. 2.35
c. 2.20 d. 13.35
___ 36. In regression and
correlation analyses, the entity on which units of measurements are taken is
known as the ______________.
a. dependent variable b. impartial variable
c. variables d.
discrete variable
_ ___ 37. Given:
:
= 10,
:
? 10, n = 12,
= Zero.01, and the computed check statistic is
2.394,
the p worth for the check is ____________________
a.
Between Zero.02 and Zero.01 b.
between Zero.Zero25 and Zero.01
c. between Zero.05 and Zero.02 d. none of
the above
_ ____38.
The _________ is the smallest stage of significance at which
might be rejected.
a. worth of
b.
p worth
c.
likelihood of committing of Sort I error d.
worth of 1 -
â¦â¦â¦.39. We are saying that pattern outcomes are important
when ____________.
a.
is just not rejected
b.
is rejected
c. is
smaller than the p worth
d. the
computed worth of the check statistic
fall within the acceptance area
___40. You carry out a speculation check a few
inhabitants imply on the premise of the next
info: the sampled inhabitants is generally
distributed, s = 100, n =25,
= 225,
=
Zero.05,
:
> 220.
The vital worth of the check statistic is __________.
a. 2.0639 b. 1.7081
c.1.7109
d. 1.96
___ ___41. You carry out a speculation check
a few inhabitants imply on the premise of the next
info: n = 50,
= 100,
= Zero.05, s = 30,
:
< 110. The computed worth of the check
statistic
is __________.
a. -2.3570 b.-1.645
c.2.3570 d.four.24264
___ ___42. We commit a Sort I error if we
________ a real null speculation.
a. fail to reject b. reject
c. settle for
d. compute
____ _43. Given:
:
? 100, the choice speculation is _________
if the check is one- sided
and
the vital worth is unfavorable.
a.
< 100 b.
> 100
c.
= 100 d.
?
100
___ ___44. If we reject a null speculation, we
conclude that the choice speculation
__________.
a. could
be true b.is
true
c. is
not true d.
is probably not true
___ ____45. You carry out a speculation check a few
inhabitants imply on the premise of the next
info:
The pattern inhabitants is generally distributed with a variable of 100, n = 25,
= 225,
= Zero.05,
:
>220. The vital worth of the check
statistic is __________.
a.2.5 b.
1.645
c. 1.7109 d.
1.96
__ _____46. Given
:
? 25,
:
> 25, n = 14,
= Zero.05,
= 36, and
= 30, the vital worth
of the check statistic is __________.
a.1.9444 b.
1.7613
c. 1.7709 d.
2.1180
_______47. Given
:
? 70,
:
> 70, n = 10,
= Zero.01,
= 49, and
= 78, the vital worth
of the check statistic is __________.
a.three.6140 b.
2.7640
c.
three.2498 d.
2.8210
___
____48. The aim of speculation testing is to assist one attain a conclusion
about
___________ by inspecting the information
contained in ___________.
a. a inhabitants; a pattern
b. an experiment ; a pc printout
c. a inhabitants; an occasion
d. a gaggle of topics; a likelihood
assertion
___
___49. The likelihood of rejecting a real null speculation can also be referred to
because the _______
for the check.
a. p worth b.
vital worth
c.
rejection area d.
stage of significance
___
____50. A null speculation is rejected on the stage of significance when the p
worth is
_________.
a. lower than or equal to ?
b. precisely equal to ? solely
c. better than or equal to ?
d. better than or equal to the vital
worth of the check statistic
___
___51. The 2 sorts of statistical hypotheses are the null speculation and the
__________hypothesis.
a. accepted b.
rejected
c. various d.
null
__
____52. The assertion of what the investigator is making an attempt to conclude is positioned
within the _____
speculation.
a. accepted b.
rejected
c. various d. null
_______53.
The _______ speculation is the speculation that's examined.
a. accepted b.
rejected
c. various d. null
_______54.
If the null speculation is rejected, we concluded that the _______ speculation is
true.
a. accepted b.
rejected
c. various d. null
_______55.
If the null speculation is just not rejected, we conclude that the ________
speculation could
be true.
a. accepted b.
rejected
c. various d.
null
_______56.
The statistic that used as a choice maker in a hypothesis-testing process
is named the __________.
a. check statistic b. pattern
statistic
c. unbiased statistic d.
related statistic
_______57.
The rejection of a real null speculation is named the ______ error.
a. commonplace b. Sort I
c. vital d.
Sort II
_______58.
The amount that provides the likelihood that a false null speculation might be
rejected is
known as the ________ of the check.
a. energy b.
likelihood of a Sort II error
c. significance stage d.
likelihood of a Sort I error
______59.
Which of the next statements is just not essentially true when utilized to a
check
statistic?
a. It's usually distributed with a imply
of Zero and a variance of 1.
b. It's computed from pattern information.
c. Its vital worth(s) is/are obtained
from applicable tables of its sampling distribution.
d. It serves as a choice maker.
_______60.
Which of the next statements is just not true when utilized to the extent
significance?
a. It's all the time equal to the likelihood of
committing a Sort I error.
b. It ought to all the time be established previous to
gathering and analyzing the information.
c. It's all the time bigger than the p worth.
d. Beneath the curve of the related sampling
distribution, it's the space above the rejection
area.
Half D:Should present all of your work step-by-step to be able to obtain the
full credit score; Excel is just not allowed. (61-71)
61. Use the next
info from anormal inhabitants with imply ? = 52 and variance ?2= 22.5 to
calculate the next questions.
a) discover P (X >55 )
b) discover P
c) discover P
62.
A random pattern from a inhabitants
with imply and commonplace deviation produced the next pattern info:
n =110 x = 699 s = 20.four
a)
Discover a 95% confidence interval for the imply
?. Interpret this interval.
b)
Discover a 99% confidence interval for the imply
?. Interpret this interval.
63.
Think about the next speculation check.
Ho: Âµ = 17
Ha: Âµ ? 17
A pattern of
25 provides a pattern imply of 14.2 and pattern variance of 25.
a)
At ? = Zero.05, what's the
rejection rule?
b)
Compute the worth of the check
statistic
c)
What's the p-value?
d)
What's your conclusion?
64.
Think about the next
speculation check.
Ho: ? = 15
Ha: ? ? 15
A pattern of 50
provides a pattern imply of 14.2 and pattern commonplace deviation of 5.
a) At ? = Zero.02, what's the
rejection rule?
b) Compute the worth of the check statistic z.
c)
What's the p-value?
d)
What's your conclusion?
65.
Think about the next speculation
check
Ho: Âµ ? 10
Ha: Âµ < 10
A pattern of 50 supplies
a pattern imply of 9.46 and pattern variance of four.
a)
At ? = Zero.05, what's the
rejection rule?
Reject null if z
< 1:645
b)
Compute the value of the test
statistic
c)
What is the p-value?
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 (R2).
f)
Interpret the coefficient of
determination (R2).
g)
Calculate the adjusted
coefficient of determination (Adjusted R2).
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 t-ratio
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 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)
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?
69.
Computer output:
Coefficients
Std. Error
t-Stat
P-value
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
Se =12.86986
R-sq = 0.862263
R-sq(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 Ha: B1 > Zero, what statistical resolution ought to
be made at 5% stage.
f)
What's the commonplace error of
estimate? Can you utilize this statistic to evaluate the modelâs match? In that case, how?
g)
What's the coefficient of
dedication, and what does it inform you in regards to the regression mannequin?
h)
What's the coefficient of
dedication, adjusted for levels of freedom? Clarify how this statistic and
the statistic referred to partly (f) aid you to find out how nicely the mannequin
matches the information.
i)
Take a look at the general utility of the
mannequin. What does the p-value of the check statistic inform you?
70.
For the next ANOVA desk are the outcomes from treating four cultures with
6 observations for every tradition. The enzymes are contained in check tubes with
differing ranges of enzymes utilized.
a) Please fill within the clean.
Supply of Variation
df
SS
MS
F
Therapy
180
Error
60
Complete
b) What are the null and alternate
hypotheses?
c) What's your resolution rule, Use
d) Point out your statistical resolution.
e) Is
there a distinction among the many means?
71. A metropolitan bus system samplerâs rider counts on one
of its specific commuter routes for every week. Use the next information to ascertain
whether or not the rider ship is evenly balanced by day of the week. Let
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Rider Depend
10
34
21
57
44
a)
Is the ?2value
important at 5% stage of significance?
b)
Write the
conclusion for this query.