For the data below provided is two samples purportedly from the same population.

Question

For the data below provided is two samples purportedly from the same population. Use an F-ratio test to prove if the variances are equal.

20.0129 17.52245 21.3001 21.24338 23.501 18.7252 20.3007 20.55718 19.5348 18.73537 21.4347 18.41443 19.5648 20.75355 17.8622 20.60235 22.3716 23.70248 18.3137 16.05623 20.744 18.60958 18.2201 20.17798 20.2857 19.42237 18.9353 18.84923 22.4136 20.47993 16.8108 19.68603 20.5379 18.15653 22.2048 21.09724 21.9284 17.88835 22.308 19.66373 20.7615 21.97949 19.5614 15.72028 21.5306 22.88234 17.7152 20.12359 23.1025 19.63148 19.2705 18.89889 17.9134 20.71555 23.2732 19.19001 23.1234 19.27084 15.8366 22.69945 19.08605 20.80717 18.33657 21.67572 20.06486 19.83621 20.70955 19.76088 17.92087 20.20504

Explanation / Answer

Standard deviation of sample 1 s1= 2.047

n1= 30

Standard deviation of sample 2 s2=1.6594

n2= 40

Here

H0: 1= 2

Ha : 1 2

F = s12/s22= (2.047)2 /(1.6594)2 = 1.522

Here alpha = 0.05 , dF1= 30 , dF2= 40

F0.05,30,40 = 1.7444

Fcritical > F so there is variance of two samples is equal.

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