Chapter 9 Hypothesis Testing

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Chapter 9Hypothesis Testing
Testing Hypothesis about µ, when the s.t of
population is known
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THREE WAYS TO STRUCTURE THE HYPOTHESIS TEST
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Lets revisit the researcher who believes that
the mean length of a cell phone call has
increased from its June, 2001 mean of 2.62
minutes. What is the null and alternative
hypothesis?
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We will assume the length of the phone call is
still 2.62 minutes. Suppose we take a simple
random sample of 36 cell phone calls. Assume the
standard deviation length of a phone call is
known to be 0.78 minutes. What is the sampling
distribution of the sample mean?.
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We will reject the null hypothesis if the sample
mean is too far from the assumed population
mean. What does this mean? We might define too
far as too many standard deviations from the
assumed population mean
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For example, we might reject the null hypothesis
if the sample mean is more than 2 standard
deviations above the population mean. Why?

Area 0.0228
z
0 1 2
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If the null hypothesis is true, then 1 - 0.0228
0.9772 97.72 of all sample means will be less
than
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Because sample means greater than 2.88 are
unusual if the population mean is 2.62, we are
inclined to believe the population mean is
greater than 2.62.
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Step 1 A claim is made regarding the population
mean. The claim is used to determine the null and
alternative hypotheses. Again, the hypothesis can
be structured in one of three ways
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The critical region or rejection region is the
set of all values such that the null hypothesis
is rejected.
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Step 4 Compare the critical value with the test
statistic
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Step 5 State the conclusion.
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EXAMPLE The Classical Method of Hypothesis
Testing A can of 7-Up states that the contents of
the can are 355 ml. A quality control engineer
is worried that the filling machine is
miscalibrated. In other words, she wants to make
sure the machine is not under- or over-filling
the cans. She randomly selects 9 cans of 7-Up
and measures the contents. She obtains the
following data.
351 360 358 356 359 358 355 361 352
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EXAMPLE The Classical Method of Hypothesis
Testing
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A P-value is the probability of observing a
sample statistic as extreme or more extreme than
the one observed under the assumption the null
hypothesis is true.
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Hypothesis Test Regarding µ with s Known
(P-values)
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Step 1 A claim is made regarding the population
mean. The claim is used to determine the null and
alternative hypotheses. Again, the hypothesis can
be structured in one of three ways
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Step 3 Compute the P-value.
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EXAMPLE Testing a Hypothesis Testing Using
P-values
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EXAMPLE Testing a Hypothesis Using P-values A
can of 7-Up states that the contents of the can
are 355 ml. A quality control engineer is
worried that the filling machine is
miscalibrated. In other words, she wants to make
sure the machine is not under- or over-filling
the cans. She randomly selects 9 cans of 7-Up
and measures the contents. She obtains the
following data.
351 360 358 356 359 358 355 361 352
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