Math 252B Exam 2 Questions: Name and ID
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EXPACTATİON(5P) |
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NOT:
SHOW ALL YOUR WORK. ANSWERS WITHOUT WORK WILL NOT BE GRADED!!!
1.[25
points] The following data show the age of top executive for major markets of
food, retail, and personal care products
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Company |
Category |
Executive |
Age |
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X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 |
FOOD FOOD FOOD PERSONEL-CARE PERSONEL-CARE PERSONEL-CARE PERSONEL-CARE RETAİL RETAIL RETAIL RETAIL RETAIL |
A B C D E F G H I F K L |
48 51 59 51 64 67 59 59 53 55 57 58 |
a)At
the 0,05 level of significant, is there a significant difference in the mean
age of executives for the three categories of companies
b)
Set up the ANOVA table for this problem
SOLUTION:
a)20 point
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Anova: Single Factor |
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SUMMARY |
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Groups |
n |
Sum |
Average |
Variance |
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FOOD |
3 |
158 |
52,66667 |
32,33333 |
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PERSONEL-CARE |
4 |
241 |
60,25 |
48,91667 |
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RETAIL |
5 |
282 |
56,4 |
5,8 |
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SSRT=99,6333 |
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b)5 point |
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ANOVA |
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Source of Variation |
SS |
df |
MS |
F |
F crit |
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Between Groups |
99,63333 |
2 |
49,81667 |
1,91099 |
4,25649473 |
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Within Groups |
234,6167 |
9 |
26,06852 |
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Total |
334,25 |
11 |
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Since F<FCritical then we can not reject the
hypothesis which is saying there exists a significant age difference amongst
the top executive managers of these there sectors managers.
2.[20
points] Consider the table and answer
the following questions
POPULATION
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Element |
1 |
2 |
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1 2 3 4 5 |
21 28 18 20 26 |
20 26 18 20 24 |
a) Compute the difference value
for each element
b)
Compute average of d
c)
Compute the standard deviation of d
d)
Test whether there is any increase from population 1 to 2
Solution:a)
POPULATION
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Element |
1 |
2 |
d |
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1 2 3 4 5 |
21 28 18 20 26 |
20 26 18 20 24 |
1 2 0 0 2 |
b)
c)
d) In order to test the existence of any increase from
population 1 to population 2 we need the following Hypothesis test.
We need
since 2,236>2,132
we Reject Null Hypothesis. So there is not any increase from population1 to
population
3.[20
points] At t test for a mean uses a
sample of 15 observations. Find the t test statistic value that has a P-value
of 0,05 when the alternative hypothesis is a)Ha: Population Mean >0, b) Ha: Population
Mean is not equal to zero b) Ha: Population Mean <0
Solution:
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a)
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b)
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c)
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4.
[20 points] the national Association of Home Builders provided data on the cost
of the most popular home remodeling projects. Sample data on cost in thousands
of dollars for two types of remodeling projects follow.
Kitchen Master Room
25,2 18,0
17,4 22,9
22,8 26,4
21,9 24,8
19,7 26,9
23,0 17,8
19,7 24,6
16,9 21,0
21,8
23,6
a)
Develop a point estimate of the difference between the population mean remodeling
costs for the two types projects
b)
Develop a 90% confidence interval for the difference between the two population
means.
a) 
21,2 (Kitchen) 
22,8 (Master Room) so Point Estimate of the difference
between the population mean remodeling costs for two types project is
21,2-22,8=-1,6
b)
5. [20 points] Briefly explain the meaning of
the following terms: Type 1 and Type 2 errors, P-Value
Solution:
Type1 Error: Rejecting Null Hypothesis When the Null
Hypothesis is true
Type2 Error: Retaining Null Hypothesis When the
Alternative Hypothesis is true
P-Value: Probability of making type1 error after
rejecting Null Hypostasis