A Smallville statistician wanted to test if the population v

A Smallville statistician wanted to test if the population variance in policeman monthly overtime hours is higher than the population variance in fireman monthly overtime hours. A random sample of seven firemen showed a standard deviation of 7 monthly overtime hours whereas, a random sample of 5 policemen showed a standard deviation of 12 monthly overtime hours. At the .01 level of significance, is there more variation in policeman monthly overtime hours?

Solution

Answer to the question)

Claim : Policemen overtime > firemen overtime

.

Given:

Policemen data =

n1 = 5

s1 = 12

Firemen data =

n2 = 7

s2 = 7

.

test statistic

F = s1^2/ S2^2

F = 12^2 / 7^2

F = 144 /49

F = 2.9388

.

df numberator = 5-1 = 4

df denominator = 7-1 = 6

alpha = 0.01

F critical can be obtained from the F table : 9.15

F critical = 9.15

.

Inference: Since F statistic 2.9388 < F critical 9.15, we fail to reject the null that the two samples have equal standard deivation

Conclusion: there is no statistically significant evidence to support the claim that the variance of overtime work hours of polimen are higher than the overtime work hours of the firemen