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Chapter 9
Hypothesis Testing
Testing Hypothesis about µ, when the
s.t of population is known
THREE WAYS TO STRUCTURE THE
HYPOTHESIS TEST:
Let’s 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?
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?.
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
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
0
1
2
z
If the null hypothesis is true, then 1 - 0.0228 =
0.9772 = 97.72% of all sample means will be
less than
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.
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:
The critical region or rejection region is the
set of all values such that the null hypothesis is
rejected.
Step 4: Compare the critical value with the test
statistic:
Step 5: State the conclusion.
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 overfilling 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
EXAMPLE The Classical Method of Hypothesis
Testing
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.
Hypothesis Test Regarding μ with σ Known
(P-values)
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:
Step 3: Compute the P-value.
EXAMPLE Testing a Hypothesis Testing Using
P-values
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 overfilling 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