Q: Use the following information to determine whether or not you should reject or fail to reject the null hypothesis:
SBetween=100
SSWithin=500
n per group=20 (i.e. total n=80)
H0: µ1= µ2= µ3= µ4
H1: At least one mean is different
α=.05
A: I constructed a table to help me organize my work but I don't know if I filled it out correctly
sum of squares df MS F
Between 100 19 5.3 0.64
Within 500 60 8.3
Total 400 79
ssTotal=500-100=400
Msbetween = 100/19=5.3
Mswithin=500/60=8.3
F= 5.3/8.3= 0.64
Then I located F critical under the F table as the value of 1.98.
My professor said when F calculated is less than F critical, you fail to reject.
F calculated= 0.64
F critical= 1.98
0.64<1.98, so fail to reject?
To determine whether to reject or fail to reject the null hypothesis, we need to compare the calculated value of F to the critical value of F for a given significance level.
The degrees of freedom (df) for Between is (number of groups - 1) = 4 - 1 = 3.
The degrees of freedom for Within is (total number of observations - number of groups) = 80 - 4 = 76.
First, we need to find the critical value of F. Looking up the critical value of F in a table at α = 0.05 with 3 and 76 degrees of freedom, we find that the critical value of F is approximately 2.80.
Since the calculated value of F (0.64) is less than the critical value of F (2.80), we fail to reject the null hypothesis.