CK-12 Probability and Statistics - Advanced

11.1. The F-Distribution and Testing Two Variances http://www.ck12.org

Supplemental Links

• Distribution Tables http://www.statsoft.com/textbook/sttable.html

Review Questions

1. We use theF-Max test to examine the differences in the ___ between two independent samples.


2. List two differences between theF- and the Student’st-distributions.


3. When we test the differences between the variance of two independent samples, we calculate the ___.


4. When calculating theF-ratio, it is recommended that the sample with the sample variance be placed in
   the numerator and the sample with the sample variance be placed in the denominator.

Suppose the guidance counselor tested the mean of two student achievement samples from different SAT preparatory
courses. She found that the two independent samples had similar means, but also wants to test the variance associated
with the samples. She collected the following data:

SAT Prep Course 1 SAT Prep Course 2

n= 31 n= 21

s^2 = 42. 30 s^2 = 18. 80

5. What are the null and alternative hypotheses for this scenario?


6. What is the critical value with aα=.10?


7. Calculate theF-ratio.


8. Would you reject or fail to reject the null hypothesis? Explain your reasoning.


9. Interpret the results and what the guidance counselor can conclude from this hypothesis test.


10. True or False: The test of the null hypothesisH 0 :σ 12 =σ 22 using theF-distribution is only appropriate when
    it can be safely assumed that the population is normally distributed.

Review Answers

1. Variance


2. Answers may vary but could include:
   
   
   1. We use thet-distribution when testing the difference between the means of two independent samples and
      theF-distribution when testing the difference between the variances of two independent samples.
   
   
   2. Thet-distribution is based off of one degree of freedom and theF-distribution is based off of two.
      3.F-distributions are not symmetrical,t-distributions are.
      4.T-values range from−∞to∞whileF-ratios range from zero to∞
      3.F-ratio
   
   
   
   


3. larger, smaller
   5.H 0 :σ 12 =σ 22 orσ 12 /σ 22 = 1 ,Ha:σ 126 =σ 22 orσ 12 /σ 226 = 1


4. 
   
   
   
   2. 04
   
   
   
   


5. 
   
   
   
   2. 25
   
   
   
   


6. We would reject the null hypothesis because the calculatedFratio( 2. 25 )exceeds the critical value( 2. 04 ).