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Lecture 9
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November 19, 2015
Hypothesis Testing Review:
 M (sample mean) is an unbiased estimator of μ (population mean) //
this statement means that on average, the average sample mean will
be equal to the population mean
 σM speci%es the di&erence between M and μ due to chance
 zscore test quanti%es inferences about μ
z = M μ / σM
= obtained di&erence between data H0 / expected di&erence due to
chance.
 for normally distributed zscores, use the unit normal table to
determine critical z required to reject H0
z vs. t
 to use z, population variance (σ2) must be known to calculate
standard error (σM)
z = M μ / σM
more often than not, σ2 is unknown
solution use sample variance (s2) to estimate (σ2)
S2 = ss/n1
then use s2 to estimate standard error
SM = √s2/n
To test hypotheses when σ2 is unknown use ttest
t = m – μ / SM
Determine critical value of t using the t distribution table
Df and the tdistribution
 degrees of freedom (df) the number of scores in a sample that are
free to vary
df= n1
 unlike the zdistribution (always normally distributed), the shape of
the tdistribution varies as a function of df
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As sample size goes does, so does degrees of freedom and the curve
Use t because you don’t know the population variance
Using the tdistribution table:  df
 one tailed (predicting direction whether there is an increase or
decrease) or two tailed test
α (will tell us the alpha level)

Hypothesis Testing with T
Example: Research Question – Does exposure to eyespot patterns
a&ect the behaviour of motheating birds.
Procedure and results:
n= 9
time = 60 min
Dependent Variable = time in plain side
M = 36 min
SS = 72
Step 1: State the hypothesis about the unknown population
Null hypothesis the treatment has no e&ect
H0 = μ plain side = 30 min
Alternative hypothesis the treatment has an e&ect
H1: μ plain side ≠ 30 min
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Step 2: Located the critical region based on a 2tailed test, α = 0.05
Step 3: Calculate the test statistic (t)
Step 4: Make a decision
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