Professor Charles Kingsfield of Harvard University is concerned for the graduate

Question

Professor Charles Kingsfield of Harvard University is concerned for the graduates of the Law School. He claims the variation in the salaries of his graduates is more than the variation in the salaries of graduates of other institutions. So, he conducts a sample of 30 salaries of his graduates and finds a variance of $8324. He then conducts a sample of 30 salaries of other graduates and finds a variance of $2862. Can he conclude that Harvard Law graduates have salaries that vary more than the salaries of other graduates at a .05 level of significance?

Explanation / Answer

Given that,
sample 1
s1^2=8324, n1 =30
sample 2
s2^2 =2862, n2 =30
null, Ho: ^2 = ^2
alternate, H1: ^2 > ^2
level of significance, = 0.05
from standard normal table,right tailed f /2 =1.861
since our test is right-tailed

we use test statistic fo = s1^1/ s2^2 =8324/2862 = 2.91
| fo | =2.91
critical value
the value of |f | at los 0.05 with d.f f(n1-1,n2-1)=f(29,29) is 1.861
we got |fo| =2.908 & | f | =1.861
make decision
hence value of | fo | > | f | and here we reject Ho

ANSWERS
---------------
null, Ho: ^2 = ^2
alternate, H1: ^2 > ^2
test statistic: 2.91
critical value: 1.861
decision: reject Ho
we have enough evidence to support the claim,harvard law graduates have salaries that vary more than other graduates

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