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MI12 Exam3
Name
100points total
Show all logical work when ever possible. Write neatly, if I can't read it can't grade it!
Box your answers!
Good Luck!
I. Express the null hypothesis Hoand the alternative hypothesis H, in symbolic form.
(3 points each)
a. Burritos Inc. claims that their burrito, the "Conquistador" average weight is less then 1602. Use
the true average weight of the "Conquistador" O
p,
b. The principal of a middle school claims that test scores of the seventh-graders at her school vary more
than the test scores of seventh-grades at a neighboring school, which have variation described by
a = 14.7
fi*:
a
.
r
v
=i+b
7
14.4
11. Multiple choices. Circle the right answer.
( 3 points each)
a. You have conducted a hypothesis test and found that p-value is 0.05. Based on t h ~ Information
s
you know that you cannot reject the null hypothesis if.
J
/'
; Lei e c f f f , ~h CIY\
iii.
b.
a = 0.05
You have calculated the chi-square test statistic and determined that
X2
= -5.37 . Therefore,
you will know that you
i. Automatically reject Ho
to reject Ho
the c a l c u l a t i o g
c
Select the correct hypothesis for testing the claim that the proportion of male voters (M) that
support gun control is at least as large as the proportion of female voters (F) that support gun
control.
PO
:pM-pF=0, H ~ : P M - P F < ~
_
_
1
-
iii. Ho :pM-p,=O, Ha :PM-PF
>O
iv. Ho :pM-p, <O, Ha :pM-pF < O
Page 1 of 6
May 3rd,07
p
M112 Exam3
Name
1OOpoints total
Show all logical work when ever possible. Write neatly, if I can't read it can't grade it!
Box your answers!
Good Luck!
111. True or false questions, circle. (2 point each)
ce interval estimate for /J will always contain the corresponding point estimate
b.
c.
d.
e.
f.
g.
h.
i.
j.
The t-distribution approaches the normal distribution as the number of degrees o
T or@
When making inference about one populating mean when the value of the standard deviation
the t-score is the test statistic. a o r F
"sigman is &own,
is always a left-tad test. T o r 0
A hypothesis test involving a multinomial
The Chi-square distribution is skewed to
The value of a Chi-square statistic my be negative or positive T or
In hypothesis testing, if the test tistic falls in the critical region,
null hypothesis has
been proven to be m e . T o&
The lin
correlation coefficient for the population "rhon is always a number between 0 and 1.
T or
If x an y are highly correlated, then x is said to cause y to occur. T or
"Mun i.e. p is a Greek letter. T or
a
-
Q
@
IV. For all problems below: draw graph and shade corresponding probability, identi5 the
null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null
hypothesis, and final conclusion that addresses the original claim. You are required to due
onlyfour out of thefive problems below. Circle the oneyou will not due. ( 10 points each)
1 . In a clinical study of an allergy drug, 216 of the 404 subjects reported experiencing si&icant
relief from their symptoms. At the 0.05 si@cance level, test the claim that more than hayof
those using the drug experience relief.
?
P-P
&fol $0
+hfl+
rejpc
morf
Page 2 of 6
1 Ho
.~
P
T (5
C n&&
~ u $ ' ~ . ~ , ' P q {e Y I k d w f e
8
dyvY
$pp~yl'duff
May 3rd,07
re//r
MI12 Exam3
Name
loopoints total
Show all lonical work when ever possible. Write neatly, if I can't read it can't grade it!
Box your answers!
Good Luck!
2. The weights of 19 boxes of cereal are measured. The sample standard deviation is 0.1 8 oz. The
sample mean is 14.91 oz. We are concerned that the mean weight of all boxes may be less then
15 oz. Assume that the weights of cereal are normally distributed. Test the null hypothesis a t
the 5% sigdicance level.
-
~ r = 1 4 5. z 0 . [ f o ~ )C
,
C Y ~ ~ CVAY\
\ V ~=
= 14-I-it
-
1 4
734
v I?'
i;/.uir~i
+ = 0,oa-
=IL/jqJO?-
i-LA&:
1-1. i
q ,I
*
Jt.
~
)
=
O
~
,
)
So, p L ~ = Q . O ~ FR - e j ~ c +no
h-e m e a V I
The ~ a . dab
~
~ ~ ( u ~ ~ f L~r el.!'*
t
~
+
L ~ C I . bb
~
,g$ d
~ L I F 1'3
C ~IWCI4 IS d?
2 T - ~0
\1
3. Construct a 95% confidence interval for the mean weight of cereal boxes from above, and then
interpret.
Page 3 of 6
May 3rd,07
-
-
-
-
-
~
MI12 Exam3
Name
loopoints total
Show all 1oe;icalwork when ever possible. Write neatly, if I can't read it can't grade it!
Box your answers!
Good Luck!
4. Test the given hypothesis. Assume that the population is normally distributed and that the sample
has been randomly selected.
At a=0.05 sigdcance level test the claim that a population has a standard deviation of
random sample of 18 people yields a standard deviation of 27.1
20.3. A
Two types of flares are tested for their burning times (in minutes) and sample results are gven
5.
below. Construct a 95% confidence interval for the ddferences VX - py based on the sample
data.
Assume that the two samples are independent and that they have been randomly selected.
ne
Brand X
n = 35
X = 19.4
s = 1.4
n=40 -
X = 15.1
s = 0.8
r'nbrvd
f i e d 0I ' e r e u c . e
e0nfl.dLMl-e
esh'mqk
ar
b c ? - w ~ ~ ~ . -Ay
(
1'5 b c k w ~
-
( % - x ~ ) - ~ c /-Myd(Z....
l,,
-FC)t~
Page 4 of 6
4-h
.
..
I. 1 r - .
pPw
iq,
mqaq 5
are &,(&rw\~a~3"'07
I
M112 Exam3
Name
100points total
Show all logical work when ever possible. Write neatly, if I can't read it can't grade it!
Box your answers!
Good Luck!
V.
Use the data set below. ( 15 points total)
a) Find linear correlation coefficient r, test whether or not the gven r represents a si@cant
correlation. Don't forget to set your hypothesis. Use a sigmhance level of 0.05.
linear
b) Use the given data to find the equation of the regression line. Round the final values to three
sigdicant d~gits,if necessary.
c) Using regression equation from part (b) above relating attitude rating (x) and job performance
rating (y) for the employees of a company, what is the best predicted job performance rating for a
person whose attitude rating is 80? How about loo? Do you th.mk using a rating of 100 for
attitude gives accurate results why or why not?
Managers rate employees according to job performance and attitude. The results for several
randomly selected employees are given below.
Performance
Attitude
Page 5 of 6
59
72
6 3
67
65
78
69
82
58
75
77
87
76
92
69
83
70
87
64
78
May 3rd,07
M112 Exam 3
Name
1 OOpoints total
Show all logical work when ever possible. Write neatly, if I can't read it can't grade it!
Box your answers!
Good Luck!
VI.
Use a x2 test to test the claim that in the given contingency table, the row variable and the column
variable are independent.
Use the sample data below to test whether car color affects the likelihood of being in a n accident. Use
a significance level of 0.01 .
Red Blue White
Car has been in
accident
Car has not been
Page 6 of 6
May 3rd,07
Continuation from number V.
Note instead of number 4 do this problem.
Test the indicated claim about the means of two populations. Assume that the two samples are independent that they have
been randomly selected.
4. Two types of flares are tested for their burning times (in minutes) and sample results are given below.
Brand X
Brand 1'
= 35
n = 40
X = 15.1
s = 0.8
n
-
x = 19.4
s = 1.4
Refer to the sample data to test the claim that the two populations have equal means. Use a 0.05 significance level.