August 30 - Chi-square - Test for a Variance and Standard Deviation

Last Thursday, Ms. Macatigos gave us again a quiz. But this time it’s about x²- Test for a Variance and Standard Deviation. Its quite difficult this time compare to the quiz about z- test for proportion. But I’m very glad when I receive my paper and get only a mistake. But it’s really confusing.

Let me give you an example about X²- Test for a Variance and Standard Deviation. In x²- Test for a Variance and Standard Deviation, you will first state the hypotheses, find the critical value, solve for the test value, make the decision and summarize the results.                                                          

                   

PROBLEM:

         

The calcium content of the Calci- Milk brand is known to be normally distributed with a variance greater than 1.6. If a random sample of 30 has a variance of 1.2, is there enough evidence to support the claim?  Use a 0.95 significance level.                             

Solution:

       Step 1: State the Hypothesis

                   * H₀: σ² ≤ 1.6

                   * H_I: σ² > 1.6 (claim)

      

      Step 2: Solve for the Critical Value

                 *Alpha=0.95, right tailed test, C.V= 17.708

    

      Step 3: Solve for the test value

               X² = (n-1) (s²)/ σ²

                        = (29) (1.2)/ 1.6

                          = 21.75

      Step 4: Make the decision

                 *Reject the null hypothesis since the test value falls in the critical region.

      Step 5: Summarize the results

                 *There is enough evidence to support the claim.

          I hope you agree with my solution.

By: Dustin Joshua A. Esquia III- Gold