� More about All expected frequencies
2
� test for independence and E i should be greater than 5
2
� goodness of fit test :
� Z test when the population variance
� : Population mean H
0
: � � �0
H
1: � �0
2
� is known :
� , � � �0 ( for 1-tailed test ), � � �0
( for 2-tailed test )
H
0 is rejected if the p -value is less than the significance level
H
0 is not rejected if the p -value is greater than the significance level
� One sample t test when the population variance
� : Population mean H
0
: � � �0
H
1: � �0
2
� is unknown :
� , � � �0 ( for 1-tailed test ), � � �0
( for 2-tailed test )
H
0 is rejected if the p -value is less than the significance level
H
0 is not rejected if the p -value is greater than the significance level
� Paired t test : d �x � y : Difference between each pair of data from two variables x and y
H : � � 0
0
1 d
H : � � 0 , � � 0 ( for 1-tailed test ), � � 0 ( for 2-tailed test ) d d
H
0 is rejected if the p -value is less than the significance level
H
0 is not rejected if the p -value is greater than the significance level
d
� Test involving binomial distribution : X ~ B ( n, p ) p H
0
: � p0 p� , p� p0 x : Observed value of X
H
1: p0
P ( X � x) for H
1: p� p0 or P ( X � x) for H
1
: p� p0 : p -value under X ~ B ( n, p0
)
H
0 is rejected if the p -value is less than the significance level
H
0 is not rejected if the p -value is greater than the significance level
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