Question

SD 1= 45.1

SD 2 = 82.1

A. 5. F test for 2 standard deviations (Covered in Module 4 - Topic 14) Diagram [1] Hypotheses 12] Ho Hi Calculation of test statistic [1] Reject or fail to reject [1]. Formal statement [1]

smalle size is 31

Answer 1

Given     
n₁ = 31     
s₁ = 45.1     
s₁² = 2034.01     
     
n² = 31     
s₂ = 82.1     
s₂² = 6740.41     
     
Let α = 0.05  5% level of significance   
Let σ₁ , σ₂ be the population standard deviations     
     
Hence null and alternative hypothesis are      
Ho : σ₁² = σ₂²     
H1 : σ₁² ≠ σ₂²     
     
We find the critical F-value from the F-tables for α=0.05     
α/2 = 0.025 , 1- α/2 = 0.975     
and degrees of freedom (n1 -1 = 30) and (n2 - 1 = 30)     
Since this is a two way test, we get two F-crit values     
F1 = F.INV(0.025, 30, 30) = 0.482    
F2 = F.INV(0.975, 30, 30) = 2.074     
Thus we reject Ho if F-calc < 0.482 OR F-calc > 2.074

Rejection Region 0.175 0524 0874 .223 573 9222271 2.271 (Las(A 0.874 1.573 1.922 ::@.Afii. F 0.482 F-2.074

We now calculate the F-statistic as    

F- calc- 2034.01 0.3018 6740.41

F-calc = 0.3018  (F test statistic)   
0.3018 < 0.482
that is F-calc < F1     
Hence, we reject Ho     
     
Formal Statement     
There is sufficient statistical evidence at 5% level of significance that      
the there is a difference between the two variances.