Question

An experiment involving disinfectants is repeated 15 times each for two different cleaning solutions. The first solution had a sample mean of 3.73 and sample standard deviation of 2.781 and the second solution had a sample mean of 4.8 and a sample standard deviation of 0.1715. Assuming both populations are normal, find the observed level of statistical significance that the population variances are different.

Answer 1

Since you have not mentioned the level of significance so I will assume it 0.05

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.05

F= (s1)^2/(s2)^2

F= (2.781)^2/(0.1715)^2

F= 262.9503

df1= n1-1= 15-1=14

df2= n2-1= 15-1=14

F critical= 2.48

Since F critical is SMALLER than Fcal we therefore REJECT null hypothesis H0 and

Conclusion: We have sufficient evidence to conclude that the population variances are different.