Statistical Methods

8.4.1.Example

Unit 8 - F-Distribution

8.4.Testing for the equality of variances
Example 2
To compare the variations of fish can weights manufactured by two plants, a random sample of 32 fish cans taken from the first plant gave variance of 25gm² and a random sample of 42 fish cans taken from the second plant gave variance of 40gm². Does the values support the equality of variances at 5% of significance?
Solution
F test statistic is used to test for equality of variances.
Here we have larger variance for the second plant . Hence take s₁²= 40, n₁=40, s₂²=25, n₂=32.

• H₀ : σ₁²= σ₂² (No significant difference between Variances)
• H₁ : σ₁²≠ σ₂² (Significant difference between Variances)
• Fix α =0.05 Say
• Test statistic: F= s₁²/ s₂² where s₁² is the larger sample variance

= 40/25

F_(cal) = 1.60

F_(tab) at (n₁-1, n₂-1)= (39,24)df at 5% =1.79 (approximately)

• Decision Rule: Since F_(cal)=1.40<F_(tab)=1.79 ,Null hypothesis is accepted.