MBAD 51415142

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MBAD 5141/5142

• Hypothesis testing

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Outline for todays class

• Homework Questions
• Hypothesis Testing Basics
• One-tailed tests/p-values
• Two-tailed tests/p-values

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The Overview of Testing

• The Process
• Craft a problem statement and specific research
  questions.
• For each research question, translate it into an
  either or situation the Null and Alternative
  hypotheses.

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Null and Alternative Hypotheses

• The Null Hypotheses
• What we do not want to happen
• The conclusion we will draw unless
• compelling evidence convinces us otherwise.
• The no knowledge condition.
• There is no difference between the groups.

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Null and Alternative Hypotheses (continued)

• The Alternative Hypotheses
• What we want to happen
• The conclusion we will draw if compelling
• evidence convinces us there is a difference.
• The new knowledge condition.
• There is a difference between the groups.

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Null and Alternative Hypotheses (continued)

However, we cant just accept any amount of
difference between the sample groups and conclude
that there is a difference between the
populations. We want to know that the amount of
difference we have observed is reasonably beyond
what might be caused by sampling error. We use
probability to help us be confident in our final
decision.
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The Test Statistic

• We choose a test statistic.
• We determine what the sampling distribution of
  that test statistic is when the Null hypothesis
  is True.

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The Test Statistic (continued)

• This is like saying, if there really is no
  difference in the population, how much difference
  might I get by sampling error alone?
• Given the size of the sample and the variability
  in the populations, what amount of difference can
  I expect even if there is no true difference?

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The Rejection Region

• We next have to specify a region of the sampling
  distribution of the test statistic that
  represents an acceptable risk of rejecting the
  null hypothesis even when it is true.
• The Rejection Region

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The Rejection Region (continued)

• We set the size of this region to equal the
  acceptable probability of making this type of
  error.
• We call this probability Alpha
• Typically set at .05

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The Decision

• After our study has been conducted and the test
  statistic has been calculated we apply a
  particular decision rule.
• Reject the null if the test statistic is large
  enough that it falls in the rejection region.

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The Decision (continued)

• Falling in the rejection region means that the
  test statistic is a rare event if the null
  hypothesis were true
• It is unlikely that sampling error alone made the
  test statistic so big. It is more likely that
  there is a true difference between the groups

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Hypothesis Test Example I
Most major corporations have psychologists
available to help employees who suffer from
stress. One problem that is difficult to diagnose
is PTSD. Researchers who study the disorder often
study POWs. One study conducted in 1995
investigated 33 WWII aviator POW survivors by
submitting them to the Minnesota Multiphasic
Personality Inventory. One of the components of
the test measures levels of PTSD. The higher the
score on the test, the higher level of PTSD. It
is known that the established mean test score of
Vietnam POWs is 16. The former WWII POWs
produced a mean test score of 9.00 with a
standard deviation s of 9.32. At the 10
significance level, determine whether the true
mean PTSD score of WWII aviator POWs is less
than 16.
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Hypothesis Test Example II
A company has devised a new ink-jet cartridge for
its plain-paper fax machine that it believes has
a longer lifetime (on average) that the ones
currently being produced. To investigate this
belief, 225 new cartridges were tested by
counting the number of high-quality printed pages
each was able to produce. The sample mean and
standard deviation were found to be 1511.4 pages
and 35.7 pages respectively. The historical
average lifetime for cartridges produced by the
current process is 1502.5 pages the historical
standard deviation is 97.3 pages. At a
significance level of 0.005, test the belief that
the mean lifetime of the new cartridges exceeds
that of the old cartridges.
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Hypothesis Test Example III
OCPs and PCBs are highly toxic organic compounds
often found in fish. By law, the levels of these
compounds must be monitored. A new technique
called matrix solid-phase dispersion (MSPD) has
been developed for chemically extracting trace
organic compounds from solids. Uncontaminated
fish fillets are injected with a known amount of
OCP or PCB and then the MSPD method is used to
extract the contaminant and the percentage of
toxic compound recovery was measured. The
recovery percentages of fillets injected with OCP
are listed below 99 102
94 99 95 Do the data provide sufficient
evidence to indicate mean recovery percentages of
OCPs exceeds 85 using the new MSPD method? Test
using ?.05
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Hypothesis Test Example IV
An electric motor manufacturer must fabricate
shafts for their motors. If a shaft is out of
round then vibration will occur causing failure
in the motor. The specifications call for a
critical dimension of 224 mm. Sixteen shafts are
taken off line and tested. It was found that the
mean critical dimension was 223.047 with a
standard deviation of .089. Is this evidence that
the shafts being produce differ from the needed
critical dimension of 224?
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Hypothesis Test Example V
An experiment on the side effects of pain
relievers assigned arthritis patients one of
three over-the-counter pain medications. Of the
440 patients who took one brand of pain reliever,
23 suffered some adverse symptom. Does the
experiment provide strong evidence that fewer
than 10 of patients who take this medicine
suffer adverse symptoms? Test at 5 significance.
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Type I and II errors

• TYPE I To conclude null hypothesis is true when
  it actually is not
• TYPE II To conclude that the alternative
  hypothesis is true when it is not.