Consider the two independent random samples:
Statistics and Operational Research:
Here, F-distribution will be followed depending on H1, critical value. We have discussed it in the tablebelow:
|H1||Test Statistics||Reject H0, if|
|σ21< σ22||F =||Fcal>Fα,n2 -1, n1 – 1|
|σ21> σ22||F =||Fcal>Fα,n1 -1, n2 – 1|
|σ21≠ σ22||F =||Fcal>Fα/ 2,nL -1, nl – 1|
Example No. 13:
Test the null hypothesis of the following if the intensity of light of two bulbs manufactured by two companies A and B respectively has yield of S1 = 1.5 foot-candles, S2 = 1.75 foot-candles from a sample size of 16. Here, σ12 = σ22for alternative σ12<σ22 at the level of significance as 0.01.
Critical Value, F0.01, 15, 15 = 3.52
S1 = 1.5 foot-candles
S2 = 1.75 foot-candles
H0 is accepted and there will be no variability in intensity of light by these two bulbs.