Two economics professors decided to compare the variance of their grading proced

Question

Two economics professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
                                                Mean Grade                      Standard Deviation
Professor Welker            83.6                                                        21.6
Professor Ackerman       79.7                                                        12.0

H. At the 1% level of significance, what is the decision?

H. At the 5% level of significance, what is the decision?

Explanation / Answer

Given that,
sample 1
s1^2= 21.6^2 = 466.56, n1 =10
sample 2
s2^2 = 12^2 = 144, n2 =10
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
level of significance, = 0.01
from standard normal table, two tailed f /2 =6.541
since our test is two-tailed
reject Ho, if F o < -10 OR if F o > 6.541
we use test statistic fo = s1^1/ s2^2 =466.56/144 = 3.24
| fo | =3.24

AT 0.05 LOS,
critical value
the value of |f | at los 0.01 with d.f f(n1-1,n2-1)=f(9,9) is 6.541
we got |fo| =3.24 & | f | =6.541
make decision
hence value of |fo | < | f | and here we do not reject Ho
ANSWERS
---------------
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
test statistic: 3.24
critical value: -6.541 , 6.541
decision: do not reject Ho

AT 0.01 LOS
critical value
the value of |f | at los 0.05 with d.f f(n1-1,n2-1)=f(9,9) is 4.026
we got |fo| =3.24 & | f | =4.026
make decision
hence value of |fo | < | f | and here we do not reject Ho
ANSWERS
---------------
null, Ho: ^2 = ^2
alternate, H1: ^2 != ^2
test statistic: 3.24
critical value: -4.026 , 4.026
decision: do not reject Ho

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