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Testing of Equality of Two Variances

Consider two independent random samples from two normal populations.

  1. Set up H0 : σ21 =  σ22.
  2. Set up H1 : σ21 < σ22 or σ21 > σ22 or  σ21 ≠ σ22.

 

  1. Set up the level of significance α.

 

STATISTICS & OPERATIONS RESEARCH

In this case the test statistic follows F-distribution and depending on HI' the critical value is obtained. We list in the following:

Example 13. It is desirable to determine whether there is less variability in the intensity of light by two bulbs made by company A and company B respectively in certain locations. lf the independent random samples of size 16 of the two bulbs yield S1 = 1.5 foot-candles and S2 = 1. 75 foot-candles, test the null hypothesis σ12 = σ22 against the alternative σ12 < σ22 at the 0.01 level of significance.

 

Solution.

  1. H0 : σ12 = σ22
  2. H1 : σ12 < σ22
  3. Test statistic:

 

which follows F-distribution with degrees of freedom 15 and 15.

 

4. α = 0.01. The alternative hypothesis shows that it is left tailed test.

 

Critical value F0.01, 15, 15 = 3.52.

 

5. Given Sl = 1.5 and S2 = 1.75

 

 

6. Decision : Since Fcals < 3.52, H0 is accepted.

 

=> There is no variability in the intensity of light by two bulbs.