An instructor is interested in whether there is any variatio

An 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:

Section 1: n1 = 28, x1 = 80, s1 = 16

Section 2: n2 = 25, x2 = 75, s2 = 12

Her null hypothesis and alternative hypothesis are:

H0: ²1 = ²2 H: ²1 < ²2

(a) Determine the test statistic. Show all work.

(b) Compute chi-square for Goodness of Fit. Compare Chi-Square (test) with Critical value from table for alpha and df.

(c) Is there sufficient evidence to justify the rejection of H0 at the significance level of 0.05?

Solution

Testing the Difference Between Two Variances
Null, Ho: ^2 = ^2
Alternate, 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

b.

P-value = 0.0787

c.

We don\'t have evidence t o support the cliam