A STAT 200 instructor is interested in whether there is any

A STAT 200 instructor is interested in whether there is any variation in the final exam grades between her two classes Data collected from the two classes are as follows:

Section1: n₁ = 28, x^- = 80 , S₁ = 16

Section2: n₁ = 25, x^- ₂ =75, S₂ = 12

Her null hypothesis and alternative hypothesis are:

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. (b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit. (c) Is there sufficient evidence to justify the rejection of H0 at the significance level of 0.05? Explain.

Solution

Null Hypothesis, There Is No Significance between them Ho: ^2 = ^2
Alternate Hypothesis, There Is Significance between them H1: ^2 > ^2
Test Statistic
Sample 1
s1^2=256, n1 =28
Sample 2
s2^2 =144, n2 =25
Fo =256/144 = 1.78
| Fo | =1.78
Critical Value
The Value of |F | at LOS 0.05 with d.f F(n1-1,n2-1)=F(27,24) is 1.959
We got |Fo| =1.778 & | F | =1.959
Make Decision
Hence Value of |Fo | < | F | and Here we Do not Reject Ho
P-Value : Right Tail - Ha : ( P > 1.778 ) = 0.079
Hence Value of P 0.05 < 0.079, Here we Do not Reject Ho
here Is No Significance between them