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Unformatted text preview: to choose one over the others. But we usually don’t
use α = 0.2. And nevery a high α like α = 0.8.
The nice thing about providing pvalues is that you allow the readers to pick their own α’s
and arrive at their own conclusions quickly. Utku Suleymanoglu (UMich) Hypothesis Testing 21 / 39 What determines test results? σ is known: Two Tailed Tests Now we will discuss a slightly diﬀerent type of test. The diﬀerence is in the null and alternative
hypothesis tests:
H0 :µ = µ0
H1 :µ = µ0
These type of tests judge the claim that unknown population parameter is exactly equal to some
number. In economics, twotailed tests are performed a lot to test things like:
Whether a production technology have constant returns to scale. (population parameter=1)
Whether a job training program has any eﬀect on wages whatsoever. (population
parameter=0)
We will come back to the latter one again when we do regression analysis. Utku Suleymanoglu (UMich) Hypothesis Testing 22 / 39 What determines test results? Example
Test procedure is very similar to the onetailed tests with a few but important diﬀerences.
Suppose with your lightbulb sample (remember x = 2.5, n = 25 and σ = 1.5.) Now suppose that
¯
there is a claim that says the mean life expectancy of lightbulbs is 2.6 years:
H0 :µ = 2.6
H1 :µ = 2.6
The test statistic is going to be identical with onetailed tests:
z= 2.5 − 2.6
x − µ0
¯
= −0.33
√=
σ/ n
0.3 The test statistic calculates the relative position of 2.5 with respect to hypothesized value for µ:
2.6. You can see it is fairly close as measured by z = −0.33. Given that normal distribution is
¯
bellshaped, we know x = 2.5 draw from the distribution of X is quite probable if µ = 2.6, so we
¯
should not reject the H0 .
Key thing: Because of the equality in the null, what we consider unlikely (under the assumption
that the null hypothesis is true) can be on either tail. We will build our rejection regions on both
tails. Utku Suleymanoglu (UMich) Hypothesis Testing 23 /...
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 Spring '08
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