Question

• What is the decision at a 0.05 level of significance for each of the following tests? Hint: Find the critical value for each test; then make a decision. (Round your critical values to two decimal places.)
• 
  F(3, 28) = 2.98
  
  F(5, 17) = 2.63
  
  F(2, 10) = 4.02
  
  F(4, 33) = 2.69
  

Answer 1

SOLUTION:

From given data,

What is the decision at a 0.05 level of significance for each of the following tests? Hint: Find the critical value for each test; then make a decision. (Round your critical values to two decimal places.)

We reject H₀ at level = 0.05

if observed F > F ; n₁ , n₂

observed F ( n₁ , n₂ ) > F_0.05 ( n₁ , n₂ )

F(3,28 ) = 2.98

Here observed

F(3,28 ) = 2.98

F - critical = F_0.05 ( 3, 28)

= 2.946 ( from F-distribution table values)

Since, F-critical .we reject null hypothesis at level , = 0.05

F(5,17 ) = 2.63

F(5,17 ) = 2.63

F - critical = F_0.05 ( 5, 17)

= 2.809 ( from F-distribution table values)

Since, F < F-critical .we fail to reject null hypothesis at level , = 0.05

F(2,10 ) = 4.02

F(2,10 ) = 4.02

F - critical = F_0.05 ( 2 , 10)

= 4.1028 ( from F-distribution table values)

Since, F < F-critical .we fail to reject null hypothesis at level , = 0.05

F(4,33 ) =2.69

F(4,33 ) = 2.69

F - critical = F_0.05 ( 4,33)

= 2.6588 ( from F-distribution table values)

Since, F > F-critical .we reject null hypothesis at level , = 0.05