Serum ferritin is used in diagnosing iron deficiency. In a study conducted recently researchers disc

given that

sample standard deviation of the first population S1=52.6

sample size of the first population n1= 28

sample standard devaition of the second population S2=84.2

sample size of the second population n2= 26

alpha=0.01

Null hypothessi Ho: sigma2^2 = sigma1^2

alternative hypothesis H1: sigma2^2 < sigma1^2

test statistic is F = S2^2/S1^2

follows an F distribution with (25, 27) degrees of freedom

From F table, the critical value = 2.54

Therefore, the critical region is F > 2.54

substituting the values we get F = 84.2^252.6^2= 2.562

which is in the critical region, hence, the answer is

B. Yes, because the test value 2.56 is greater than the critical value of 2.54

Same conclusion can be reached if we reverse the alternative hypothesis, then

Null hypothessi Ho: sigma1^2 = sigma2^2

alternative hypothesis H1: sigma1^2 > sigma2^2

test statistic is F = S1^2/S2^2

follows an F distribution with (27, 25) degrees of freedom

From F table, the critical value = 0.394

Therefore, the critical region is F < 0.394

substituting the values we get F = 52.6^2/84.2^2= 0.390

which is in the critical region, hence, the answer should be

Yes, because the test value 0.390 is lessthan the critical value of 0.394

Thanks a lot

Krestik