Question

The following hypotheses are given:

H₀ : σ₁² − σ₂² ≤ 0

H₁ : σ₁² − σ₂² > 0

A random sample of nineteen observations from the first population resulted in a standard deviation of 33. A random sample of thirty three observations from the second population showed a standard deviation of 28. At the 0.05 significance level, is there more variation in the first population?

a. State the decision rule. (Round the final answer to 2 decimal places.)

Reject H₀ if F >                 .

b. Compute the value of the test statistic. (Round the final answer to 2 decimal places.)

Value of the test statistic                

c. What is your decision regarding H_o?

Answer 1

given that

s1 = 33

n1 = 19

s2 = 28

n2 = 33

degree of freedom1 = n1 -1 = 19-1 = 18

degree of freedom2 = n2 -1 = 33-1 = 32

(A) decision rule

using excel function F.INV.RT(alpha,df1,df2)

setting alpha = 0.05, df1 = 18 and df2 = 32

F critical = F.INV.RT(0.05,18,32)

= 1.94

Reject H₀ if F > 1.94

(b) Test statistic F = s1^2/s2^2

setting the given values, we get

= 33^2/28^2

=1089/784

= 1.39

(c) it is clear that F statistic value is 1.39, which is smaller than 1.94

So, we failed to reject the null hypothesis.