Download Hypothesis Testing

Hypothesis Testing
Notes
Hypothesis Testing
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Is used to determine whether the difference in two
groups is likely to be caused by chance
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If you flip a coin 30 times for example, you probably
wouldn’t be surprised if it was heads up16 times and tails
up 14 times…but you would probably be suspicious if it
was heads up 28 times and tails up only 2 times.
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Hypothesis testing will allow us to determine whether it
is likely or unlikely that there is bias in a given situation.
Hypothesis Testing Continued
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We will begin with a null hypothesis, which states that
there is no difference between the two groups being
tested.
A null hypothesis is often times the opposite of what is
expected to happen. We use the null hypothesis so that
we can allow the data to contradict it.
In a randomized controlled experiment, the null
hypothesis will always be that there is no difference in the
value of the variable for the control group and the
treatment group.
Let’s look at an example.
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A teacher wants to know if her first block class performs
better on a quiz than her fourth block class. She
compares the scores of 10 randomly chosen students in
each class.
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First Block: 76, 81, 71, 80, 88, 66, 79, 67, 85, 68
Fourth Block: 80, 91, 74, 92, 80, 80, 88, 67, 75, 78
Her null hypothesis would be: The students in first block
will have the same quiz grades as the students in fourth
block.
Example continued:
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Let’s do a five-number summary for each class:
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First Block: min = 66, Q1 = 68, median = 77.5, Q3 = 81, max =
88
Fourth Block: min = 67, Q1 = 75, median = 80, Q3 = 88, max =
92
There is a large difference in the two classes that is
unlikely to be caused by chance.
The teacher should reject her null hypothesis, which
means that students in her afternoon class do better on
quizzes.
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If a sample contains at least 30 individuals, you can use a
z-test to be more precise with your hypothesis testing.
To find the z-value of a statistic for a sample with n
individuals, a sample mean of x, a population mean of µ,
and a standard deviation σ, we do:
A large z-value will tell us to reject the null hypothesis.
If the absolute value of z is greater than 1.96, then you
can reject the null hypothesis with 95% certainty.
If the absolute value of z is less than 1.96, then you do no
have enough evidence to reject the null hypothesis.
Example
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A test prep company says that it can boost SAT scores to
an average of 1800. In a random sample of 36 students
who took the course, the average was 1745 with a
standard deviation of 210. Is there enough evidence to
reject the claim?
Example continued
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Our null hypothesis would be: There is no difference in
the sample and the population.
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Let’s find the z-value. The mean is 1800, the sample mean
is 1745, the standard deviation is 210, and n = 36:
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Because the absolute value of z is less than 1.96, you do
not have enough evidence to reject the claim with 95%
confidence.
This doesn’t mean their claim is true, but we don’t have
enough information to prove it false.
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