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MIE 364S: Methods of Quality Control and Improvement
Tutorial 0
1.
Cartons of grommets are rated at 40 pounds. Ten sample weights were obtained as
follows:
41.7
40.6
41.0
42.5
40.4
42.4
42.7
41.2
42.6
41.5
Assume the weights are normally distributed with mean
and variance
2
0.64
a)
Test the null hypothesis
41
at significance level
0.01
. Construct a
twotailed critical region and calculate the pvalue. What is your conclusion?
b)
Assuming the error of 1 pound is important to detect, find (40)
and (42)
c)
Find the minimum sample size n such that the error of 1 pound is detected by
the test in 1a) with probability
0.9
9.
2.
An experiment wishes to demonstrate that, at 100
。
C, the coefficient of static
friction of steel on steel when lubricated by a newly developed graphited oil is less
than 0.13. The measurement process is assumed to be normally distributed with
standard deviation
0.005
and the sample mean corresponding to a random
sample of size 40 is
0.128
X
a)
Formulate and test the null hypothesis at significance level
0.05
. Calculate
the p value and draw conclusions.
b)
Calculate the power of the test for
1
0.128
.
c)
Find the minimum sample size n such that the power of the test for
1
0.128
is
0.95
3.
Pipe stock is automatically fed to a cutter to produce cuts of nominal length 8.05
feet. To test the accuracy of the equipment, 12 cuts are randomly selected and
their lengths measured.
a)
Assuming the population of lengths is normally distributed, do the
measurements (in feet)
8.08
8.02
8.04
8.04
8.02
8.05
8.02
8.03
8.07
8.01
8.03
8.07
yield the conclusion, at the
0.05
level, that the nominal mean length should
be rejected?
b)
Estimate the pvalue.
4.
The mean time to repair (MTTR) a unit is the average time it takes to repair a unit
that has been taken out of service. As an illustration, consider a robot paintsprayer.
Such a unit can fail for any number of reasons; however, let us suppose that the
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View Full Documenttime to repair is normally distributed, but with unknown variance. It is claimed by
the manufacturer that the MTTR is less than 3.4 hours. With a number of the units
in operation, nine repair times are randomly selected and a t test is performed in
an effort to demonstrate the manufacturer’s claim. The following times (in hours)
are observed:
0.8
7.4
3.8
5.5
1.3
2.7
3.5
1.1
1.8
a)
Determine if the manufacturer’s claim is supported at
0.05
significance
level.
b)
Estimate the pvalue.
5.
The random variable X counts the number of bits in coded messages emanating
from a certain source. Assuming X to be approximately normally distributed, it is
desired to check the null hypothesis H
0
:
2
160000
at the
0.1
level
a)
Construct the appropriate twotailed critical region and make a decision based
upon the bit counts
4532
4606
3511
4201
3392
4639
4021
4722
3470
3100
4212
4165
b)
Estimate the pvalue.
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 Spring '12
 Makis

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