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ECO252 QBA2
SECOND EXAM
March 23, 2007
TAKE HOME SECTION
Name: _________________________
Student Number: _________________________
Class hours registered and attended (if different):_________________________
IV. Neatness Counts! Show your work! Always state your hypotheses and
conclusions clearly. (19+ points). In each section state clearly what number you are
using to personalize data. There is a penalty for failing to include your student
number on this page, not stating version number in each section and not including
class hour somewhere. Please write on only one side of the paper. You must do 3a
(penalty).
1. (Groebner, et. al.) Your company produces hair driers for retailers to sell as house brands. A design
change will produce considerable savings, but the new design will not be adopted unless it is more reliable.
For a sample of 250 hair driers with the old design, 75 failed in a simulated 1-year period. For a sample of
250 driers with the new design 50  a fail in a simulated one year period, where a is the second-to-last
digit of your student number. Use a 90% confidence level. Make sure that I know what value you are using
for a .
a) Can we say that the proportion of the redesigned driers that fail is significantly lower than that of the
driers with the current (old) design? (3)
b) Do a 95% two-sided confidence interval for the difference between the two proportions. (1)
c) After you have implemented your decision on using the new design, a newly-hired engineer recommends
another design change (the newest design) that she claims will decrease the proportion that fail even
further. For a sample of 100 driers, 18 fail in a simulated one-year period. Do a test of the equality of the
three proportions, again using a 90% confidence level. (4)
d) Follow your results in c) with a Marascuilo procedure for finding pairwise differences between the
proportions for the three designs. Assuming that there is no cost-saving in going to the newest design,
would you recommend going to it? Write a paragraph long report on your conclusions from the two
hypothesis tests and what decisions these implied. (4)
[12]
2. (Groebner et al) A ripsaw is cutting lumber into narrow strips and should be set to produce a product
whose width differs from the width specified by an amount given by a Normal distribution with a mean of
zero and a standard deviation of 0.01 inch. Because we have been getting complaints about the uniformness
of our product, we wish to verify the Normal distribution specified is correct. We cut 600  b pieces (where
b is the last digit of your student number. Our results are as follows.
Deviation from
Number of pieces
specified width
Below -0.02
0
-0.02 to -0.01
84
-0.01 to 0
266
0 to 0.01
150 + b
0.01 to 0.02
94
0.02 and above
6
a) To use a chi-squared procedure to check the distribution, find the values of E (3)
b) State and test the null hypothesis. (2)
c) We have learned another procedure that can be used to test for a Normal distribution when the
parameters are given. Use it now to verify your results. Can you say that the saw is working as advertised?
(4)
[21]
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3. (Groebner et al.) Two groups of 16 individuals were asked to do their income taxes using two tax
preparation software packages. The data is below (in number of minutes required) and may be considered
two independent random samples. To personalize the data add the last digit of your student number to
every number in the TT00 column. Use 10 if your number ends in 0. Label the column clearly as TT1, TT2
through TT10 according to the number used. Let d  TTa  TC .
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
TT00
65
51
74
89
88
96
37
66
86
54
60
45
42
55
58
38
TC
88
71
89
66
78
64
74
99
79
68
93
93
86
86
81
83
Minitab has given us the following results
Variable
TC
TT1
TT2
TT3
TT4
TT5
TT6
TT7
TT8
TT9
TT10
N
16
16
16
16
16
16
16
16
16
16
16
N*
0
0
0
0
0
0
0
0
0
0
0
Mean
81.13
63.75
64.75
65.75
66.75
67.75
68.75
69.75
70.75
71.75
72.75
SE Mean
2.60
4.76
4.76
4.76
4.76
4.76
4.76
4.76
4.76
4.76
4.76
StDev
10.40
19.05
19.05
19.05
19.05
19.05
19.05
19.05
19.05
19.05
19.05
Minimum
64.00
38.00
39.00
40.00
41.00
42.00
43.00
44.00
45.00
46.00
47.00
Q1
71.75
47.50
48.50
49.50
50.50
51.50
52.50
53.50
54.50
55.50
56.50
Median
82.00
60.00
61.00
62.00
63.00
64.00
65.00
66.00
67.00
68.00
69.00
Q3
88.75
84.00
85.00
86.00
87.00
88.00
89.00
90.00
91.00
92.00
93.00
Maximum
99.00
97.00
98.00
99.00
100.00
101.00
102.00
103.00
104.00
105.00
106.00
a) Find the mean and standard deviation of d . (1) Assume the Normal distribution in b), c), and e).
b) Find out if there is a significant difference between the mean times for the two packages, using a test
ratio, a critical value or a confidence interval.(4) (2 extra points if you use all three methods and get the
same results on all three, 3 extra (extra) points if you do not assume equal variances)
c) Test the variances of the two samples for equality on the assumption that they come from the Normal
distribution. (2)
d) Test the d column to see if the data was Normally distributed (5)
e) Actually the data above was taken from only 16 people, who were randomly assigned to use one of the
methods first. Would this mean that what you did above was correct? If not do b) over again. (3)
f) In view of the fact that the data was taken from only 16 people and dropping the assumption of
Normality, find out if there is a significant difference between the medians of the two packages. (3)
g) If you did d) e) and f), can you report on your results, indicating which result was correct? (1) [40]
Be prepared to turn in your Minitab output for the first computer problem and to answer the
questions on the problem sheet about it or a similar problem.
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4. (Extra Credit) Check your work on Minitab. Remind me that you did extra credit on your front page.
For a Chi-squared test of Independence or Homogeneity, put your observed data in adjoining columns.
Use the Stat pull-down menu. Choose Tables and then Chi Squared Test. Your output will show O and E
as a single table. You will be given a p-value for the hypothesis of Independence or Homogeneity.
For a test of Normality, when sample mean and variance are to be computed from the sample, put your
complete set of numbers in one column. . Use the Stat pull-down menu. Choose Basic Statistics and then
Normality test. Check Kolmogorov-Smirnov to get a Lilliefors test. You will be given a p-value for the
hypothesis of Normality.
For a Chi-squared test of goodness of fit, put your observed data in C1 and your expected data or
frequencies in C2. The expected data may be proportions adding to 1 or counts adding to n . Use the Stat
pull-down menu. Choose Tables and then Chi Squared Test of Goodness of Fit. Pick specific proportions or
historic counts. Observed counts is C1 and the other column requested will be C2. The computed degrees
of freedom will have to be reduced if you computed any statistics from the data before setting up the
expected count or frequency. You are warned not to use expected counts below 5.
For a test of Two Proportions, Use the Stat pull-down menu. Choose Basic Statistics and then Two
Proportions. Check Summarized Data and then enter n1 , x1 , n 2 and x 2 . Use Options to set the inequality
in the alternate hypotheses and check Pooled Estimate unless you are doing a confidence interval.
To fake computation of a sample variance or standard deviation of the data in column c1 using
column c2 for the squares,
MTB
MTB
MTB
MTB
MTB
MTB
>
>
>
>
>
>
let C2 = C1*C1
name k1 'sum'
name k2 'sumsq'
let k1 = sum(c1)
let k2 = sum(c2)
print k1 k2
Data Display
sum
sumsq
MTB
MTB
MTB
MTB
>
>
>
>
3047.24
468657
* performs multiplication
** would do a power, but multiplication
is more accurate.
This is equivalent to let k2 = ssq(c1)
This is a progress report for my data
set.
name k1 'meanx'
let k1 = k1/count(c1)
/means division. Count gives n.
let k2 = k2 - (count(c1))*k1*k1
print k1 k2
Data Display
meanx
sumsq
152.362
4372.53
MTB > name k2 'varx'
MTB > let k2 = k2/((count(c1))-1)
MTB > print k1 k2
Data Display
meanx
varx
152.362
230.133
MTB > name k2 'stdevx'
MTB > let k2 = sqrt(k2)
MTB > print k1 k2
Sqrt gives a square root.
Data Display
meanx
stdevx
152.362
15.1701
Print C1, C2
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To check your mean and standard deviation, use
`
MTB > describe C1
To check for equal variances for data in C1 and C2, use
MTB > VarTest c1 c2;
SUBC>
Unstacked.
Both an F test and a Levine test will be run.
To put a items in column C1 in order in column C2, use
MTB > Sort c1 c2;
SUBC>
By c1.
Commands like Count C1, Sum C1 and SSq C1 can be used alone without Let if the values don’t need to
be stored. In the above I have continuously named and renamed the constants k1 and k2. There are many
constants in Minitab on an invisible worksheet. (k1 …….k100 at least), so you can preserve your results by
using separate locations for subsequent computations.
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