1
Posted before class.
WEEK 14 – Wed, Dec 1
HYPOTHESIS TESTING – Prof. Thomas Page Approach
Last time we went through the example MC problems 7 – 9
toward the end of the list of
MC problems.
We went through Professor Thomas Page’s Six Steps.
Step 1 involves
settingup the two hypotheses.
This may be the most difficult step.
The textbook offers advice here.
Please reread pages 257259.
The last paragraph on
page 258 is
“Although the idea of a null hypothesis is simple, determining what the null
hypothesis should be in a given situation may be difficult.
Generally, what the
statistician aims to prove is the alternative hypothesis, the null hypothesis standing for
the status quo, donothing situation”.
Another way to look at this is to look at what Type I and Type II errors are and set up
H
0
and H
1
so that the Type I (rejecting H
0
when it is true) error is the more serious error.
Prosecutors wish to prove an accused person is guilty.
With this setup
H
0
: person is innocent
H
1
: person is guilty
then Type I error is the decision to
(a) find the person guilty when in fact he/she is
innocent.
Had you setup the hypotheses in the opposite way as
H
0
: person is guilty
H
1
: person is innocent
then Type I error is the decision to
(b) find the person innocent when in fact he/she is
guilty.
In our system of justice, we may regard error (a) as more serious than error (b).
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Extra MC Problems on Testing Hypotheses (The six steps are given with answers
in bold font.)
1  2
.
A certain prescription medicine is supposed to contain an average of 200 parts per
million (ppm) of a certain chemical.
The manufacturer wants to check whether the
average concentration μ in a large shipment is the required 200
ppm
or not.
The
manufacturer wishes to control the probability of concluding the mean is different from
200
ppm
when it is not to 0.05 or less.
A random sample of 41 portions is tested, and it
is found that the sample mean is 203.1
ppm
and the sample standard deviation is
15.23
ppm
.
Carryout the six steps for this testing problem.
Step 1.
Specify H
0
and H
1
.
(a) H
0
: μ = 200ppm
H
1
: μ
200ppm
(b) H
0
: μ
200ppm
H
1
: μ = 200ppm
Step 2.
Choose the appropriate test.
(a) lefttailed
(b) righttailed
(c) twotailed
Step 3.
Specify the significance level
of the test and determine the critical value(s).
(a) 0.05, 1.960
(b) 0.025,
1.960
(c) 0.025,
1.645
(d) 0.05,
2.021
(e) 0.025, 1.68
Step 4.
Choose the appropriate test statistic and calculate its value.
(a) 1.960
(b) 0.067
(c) 2.343
(d) 1.544
(e) 1.303
Step 5.
Compare the observed (calculated) value of the test statistic with the critical
value(s) and state the decision.
(a) Reject H
0
(Decide that the population average is different from 200ppm)
(b) Retain H
0
Step 6.
State the answer to the original business problem in managerial terms.
The
specification for concentration is μ = 200
ppm
.
The random sample for the
shipment in question has average 203.1
ppm
and standard deviation 15.23
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 Summer '10
 DennisGilliland
 Statistical hypothesis testing, Reject H0, Retain H0

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