Question

A sample of 8 observations from the population indicated that sample variance s₁² is 784. A second sample of 8 observations from the same population indicated that sample variance s₂² is 144. Conduct the following test of hypothesis using a 0.05 significance level.

  H₀: σ₁² = σ₂²
  H₁: σ₁² < σ₂²

You should use the tables in the book for obtaining the F values.
For full marks your answer should be accurate to at least two decimal places.

a)

State the decision rule.

	Reject H0 in favour of H1 if the computed value of the statistic is less than or equal to FL.
	Reject H0 in favour of H1 if the computed value of the statistic is less than FL.
	Reject H0 in favour of H1 if the computed value of the statistic is greater than FL.
	Reject H0 in favour of H1 if the computed value of the statistic is greater than or equal to FL.
	None of the above

b) Compute the left F critical value.

F_L critical value: 0

c) What is the value of the test statistic?

F-Test statistic: 0

d)

What is your decision regarding H₀?

	There is sufficient evidence, at the given significance level, to reject H0 and accept H1.
	There is insufficient evidence, at the given significance level, to reject H0 and so H0 will be accepted or at least not be rejected.
	There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesis.

Answer 1

Test Statistic :-

f = 784 / 144
f = 5.4444

Test Criteria :-
Reject null hypothesis if f <= f(1 - α , n1-1 , n2-1 )
f(1 - 0.05, 7 , 7 ) = 0.2641
f > f(1 - 0.05 , n1-1 , n2-1 ) = 5.4444 > 0.2641 , hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( f > 5.4444 )
P value = 0.9801
Reject null hypothesis if P value < α = 0.05
Since P value = 0.9801 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Part a)

Reject H₀ in favour of H₁ if the computed value of the statistic is less than or equal to F_L.

Part b)

f(1 - 0.05, 7 , 7 ) = 0.2641

Part c)

f = 5.4444

Part d)

There is insufficient evidence, at the given significance level, to reject H₀ and so H₀ will be accepted or at least not be rejected.