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

Testing the Difference Between Two Means(large samples)

Friday, August 30, 2012, we've started to discuss about the topic "Testing the difference between two means with large sample size.  Let me share to you the some of the important ideas regarding this topic.

TESTING THE DIFFERENCE BETWEEN TO MEANS (LARGE SAMPLE SIZE)

FORMULA 

There are situations where a researcher wants to determine whether there is a difference in the average age of maritime students who enrolled in a maritime program at a community college and those who enrolled at a university. In this matter the researcher is not interested in the average age of maritime students who are just beginning their course; instead he is interested in comparing the means of the two groups.

Assumptions for the test to determine the difference between the two means

1.The sample must be independent of each other.

2.The population from which the samples were obtained mus be normally distributed.

3. Standard deviation of the variable must be known or the sample size must be greater than or equal to 30.

Steps

1. State the hypothesis

2. Find the critical values 

3. Decision

4. Summary of results 

BY: JOREY MARK MILLAMENA

AUGUST 30,2012

Chi-Square Test for the Variance or Standard Deviation

Chi-Square Test for the Variance or Standard Deviation

         When analyzing numerical data, sometimes you need to draw conclusions about the population

variance or standard deviation.

         A chi-square test can be used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value. The one-sided version only tests in one direction. The choice of a two-sided or one-sided test is determined by the problem. For example: 

Finding the Critical Values using the chi-square distribution.

1.    For a two-tailed test.

a. Find the degrees of freedom. d.f. = n-1

b. Split the area (α). The area to the right of the larger value CV is α/2  and the area to the right of the smaller value is 1-(α/2)

 value at the top of Table G and find the corresponding D.F in the left column.

c. Find the α/2 and 1- (α/2)

d. The critical value is located where the columns meet.

Example: α = 0.02 , d.f. = 7

α/2= 0.01        1- α/2=0.99

C.V. = 1.239

C.V. = 12.017

1.    For a Right-tailed test

a. Find the degrees of freedom

b. Find the alpha value at the top of Table G and find the corresponding D.F. in the left column.

c. The critical value is located where the two columns meet. 

 Example: α = 0.01  , d.f. = 9

  

C.V. 14.684 

1.    For a Left-tailed test

a. Find the degrees of freedom

b. Subtract the α value from 1. the left side of the table is used because the chi-square gives the area to the right of the critical value, and the chi square statistic cannot be negative.

c. Find the 1- α value at the top of table G find the corresponding d.f. in the left column.

d. The critical value is located where the two columns meet.

Example: α= 0.05 , d.f = 5

             1-α = 0.95 

C.V. = 1.145 

Formula for chi-square test

By: Tito Nuevacobita Jr. 

       III-Gold 

A Statistician, A Singer?

 

After performing many statistical exercises, exams, assignments and quizzes, let us have a break and energize by singing this song happily.

In the tune of (It’s a small world after all)

I.             There is just one class we enjoyed so much

Where our minds think hard and compute a lot

Though the quizzes are so vast

And the problems so tough

We enjoy our advance stat

Chorus:

Oh it’s stat time after all (3x)

Come together and come all

I hope you enjoyed singing.  Let us now continue to solve statistical problems with a smiling face.

BY:JOREY MARK MILLAMENA

AUGUST 29, 2012