T Statistic Calculator

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T test calculator is used to calculate a statistical hypothesis. In this the test statistic follows a students t-distribution. This is done only when the null hypothesis is supported. t = (mean(x1) – mean(x2)) / √ (s12/n1 + s22/n2)

= difference between means of 2 samples/ (variance / sample size). 


Example 1: Using t test calculator solve the following;

X1 = 2,4,6 ; X2 = 3,6,9,12

Mean of x1 = 2+4+6/3= 12/3=4

Mean of x2= 3+6+9+12/4= 30/4 =7.5

Standard deviation for x1

1.      Sum (x1-mean x1)2 = (2-5)2+(4-5)2+(6-5)2= 9+1+1= 11

2.      Sum (x2-mean x2)2 = (3-7.5)2+(6-7.5)2+(9-7.5)2+(12-7.5)2= 20.25+2.25+2.25+20.25= 45

3.      Standard deviation x1= s12= 11/3= 9.66

4.      Standard deviation x2= s22= 45/4=11.25

T critical value

T = (mean(x1) – mean(x2))/√(s12/n1 + s22/n2)

4-7.5/√/(9.66/3+ 11.25/4) = -3.5/√6.0325=  -3.5/2.456 = - 1.425



Example 2: Using t test calculator  solve following;

X1 = 4,5.5 ; X2 = 4.5,14

 Mean of x1 = 4+5.5= 9.5/2= 4.75

Mean of x2= 4.5+14/2= 18.5/2 =9.25

Standard deviation for x1

1.      Sum (x1-mean x1)2 = (4-4.75)2+(5.5-4.75)2= 0.5625+0.5625= 1.125

2.      Sum (x2-mean x2)2 = (4.5- 9.25)2+(14 -9.25)2= 22.5625+22.5625= 45.125

3.      Standard deviation x1= s12= 1.125/2= 0.5625

4.      Standard deviation x2= s22= 45.125/2=22.5625

T = (mean(x1) – mean(x2))/√(s12/n1 + s22/n2)

4.75-9.25/√/(0.5625/2+ 22.5625/2) = -4.5/√11.421875=  -4.5/3.3796= - 1.33



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