1 You want to determine whether the variance of sales at two

1. You want to determine whether the variance of sales at two music stores (A and B) are equal. A sample of 26 days of sales at store A provides a sample variance of 800 while a sample of 21 days of sales from store B provides a sample variance of 420. Don\'t know how to do

2. Last year, the variance of the ages of the students at a small liberal arts college was 3.3 years. A recent sample of 81 students from the college provides a variance of 4.1 years. You test to see if there has been a change in the variance of the ages of the students at the college.You obtain a p-vaue of .067. At level of significance of .05, the null hypotheis should be. Here are the options for the answers

a.should be rejected

b. none of these answers are correct

c. should be revised

d. should not be rejected

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   =   1  
Ha:    sigma   =/   1  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.05   ,      
alpha/2 =    0.025          
df1 = n1 - 1 =    25         
df2 = n2 - 1 =    20          
F (crit) =    0.434696654   and   2.395940849  
              
Getting the test statistic, as              
s1 =    28.28427125          
s2 =    20.49390153          
              
Thus, F = s1^2/s2^2 =    1.904761905          
              
As F is between the two critical values, we FAIL TO REJECT THE NULL HYPOTHESIS.              

Thus, there is no signficant evidence at 0.05 level that the variances of sales at the two music stores are not equal.   [CONCLUSION]      
              
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