Transcript Statistics 10.2 - Mr. Fadoir's Website

Section 10.2
Tests of Significance
AP Statistics
March 2, 2010
Berkley High School, D1B1
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Coin Flipping Example
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Why did you doubt Mr. Fadoir’s
truthfulness?
Because the outcome of the coin flipping
experiment is very unlikely.
 How unlikely?

 .5^k,
where k is the number of flips before you
yelled.
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Supposition (a fancy way of saying
“unsupported”)
Built into the argument that “Mr. Fadoir is
pulling our collective leg” is a supposition
 What is that supposition?

 “We

suppose that the coin is fair.”
Where does the supposition show up?
 .5^k
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The Test of Significance

The test of significance asks the question:
 “Does
the statistic result from a real difference
from the supposition”
 or
 Does the statistic result from just chance
variation?”
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Significance Test Procedure
Identify the population of interest and the parameter
you want to draw conclusions about. State null and
alternate hypotheses.
Choose the appropriate procedure. Verify the
conditions for using the selected procedure.
If the conditions are met, carry out the inference
procedure.
1.
2.
3.


4.
Calculate the test statistic.
Find the P-value
Interpret your results in the context of the problem
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Example


Diet colas use artificial sweeteners to avoid sugar. These
sweeteners gradually lose their sweetness over time.
Manufacturers therefore test new colas for loss of
sweetness before marketing them. Trained tasters sip
the cola along with drinks of standard sweetness and
score the cola on a “sweetness score” of 1 to 10. The
cola is then stored for a month at high temperature to
imitate the effect of four months’ storage. Each taster
scores the cola again after storage.
What kind of experiment is this?
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Example
Here’s the data:
 2.0, .4, .7, 2.0, -.4, 2.2, -1.3, 1.2, 1.1, 2.3
 Positive scores indicate a loss of
sweetness.
 Are these data good evidence that the
cola lost sweetness in storage?

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Significance Test Procedure

Step 1: Define the population and parameter of
interest. State null and alternative hypotheses in
words and symbols.
 Population:
Diet cola.
 Parameter of interest: mean sweetness loss.
 Suppose there is no sweetness loss (Nothing special
going on). H0: µ=0.
 You are trying to find if there was sweetness loss.
Your alternate hypothesis is: Ha: µ>0.
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Significance Test Procedure

Step 2: Choose the appropriate inference procedure.
Verify the conditions for using the selected procedure.


We are going to use sample mean distribution:
Do the samples come from an SRS?


Is the population at least ten times the sample size?


We don’t know.
Yes.
Is the population normally distributed or is the sample size at
least 25.

We don’t know if the population is normally distributed, and the
sample is not big enough for CLT to come into play.
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Significance Test Procedure

Step 3: Calculate the test static and the P-value.
The P-value is the probability that our sample
statistics is that extreme assuming that H0 is
true.
x-bar=1.02, σ=1
 Look at Ha to calculate “What is the probability of
having a sample mean greater than 1.02?”
 z=(1.02-0)/(1/root(10))=3.226,
 P(Z>3.226) =.000619=normalcdf(3.226,1E99)
 µ=0,
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Significance Test Procedure

Step 4: Interpret the results in the context
of the problem.
 You
reject H0 because the probability of
having a sample mean of 1.02 is very small.
We therefore accept the alternate hypothesis;
we think the colas lost sweetness.
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Assignment
Exercises 10.27-10.37 odd, 10.45-10.55
odd
 Against All Odds Video www.learner.org,
Episode 20.

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