Your Practice Paper – Applications and Interpretation HL for IBDP Mathematics
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Statistical Tests
� Hypothesis test : H
0
: Null hypothesis
H
1: Alternative hypothesis
C : Critical value in the hypothesis test
� : Significance level
2
� � test for independence for a contingency table with r rows and c columns : n � rc : Total number of data
O ( i� 1 , 2 , , n): Observed frequencies i
E ( i� 1 , 2 , , n): Expected frequencies i v � ( r �1 )( c � 1 ) : Degree of freedom
�
2 calc n 2
( Oi
� Ei)
� � : E i�1 i
2
� test statistic
H
0
: Two variables are independent
H
1: Two variables are not independent
H
0 is rejected if
� � C or the p -value is less than the significance level
2 calc
H
0 is not rejected if level
� � C or the p -value is greater than the significance
2 calc
2
� � goodness of fit test for a contingency table with 1 row and c columns : v
�c� 1: Degree of freedom H
0
: The data follows an assigned distribution
H
1: The data does not follow an assigned distribution
H
0 is rejected if
� � C or the p -value is less than the significance level
2 calc
H
0 is not rejected if level
� � C or the p -value is greater than the significance
2 calc
� Two sample t test :
�
1
, �
2
: The population means of two groups of data
H
0
: �1 � �2
H
1: �1 �2 � , �1 � �2
( for 1-tailed test ), �1 � �2 ( 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
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