A child development researcher believes that there is higher variance in the IQ

Question

A child development researcher believes that there is higher variance in the IQ of children diagnosed with Attention Deficit Disorder, but he only wants to report his theory if he observes a sample variance that is significantly higher than expected. The experimenter conducts several IQ tests on ADD children and finds that the standard deviation of his sample is 20 points. It is believed that the standard deviation of IQ scores in the general population is 15 points.

Suppose that researcher’s sample is made up of 25 children and he wants to test his hypothesis against a control group of non-ADD children. Suppose the control group is made up of 30 children and its standard deviation is 15. Test the claim that the standard deviation of the ADD group is greater than the control group.

Explanation / Answer

We se the alpha level to 0.05.

Let

sigma1 = population standard deviation of ADD children
sigma2 = population standard deviation of non-ADD children

Formulating the null and alternative hypotheses,              
              
Ho:   sigma1^2 / sigma2^2   <=   1  
Ha:    sigma1^2 / sigma2^2   >   1  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical F, as alpha =    0.05   ,      
alpha =    0.05          
df1 = n1 - 1 =    24         
df2 = n2 - 1 =    29          
F (crit) = 1.90053131            
              
Getting the test statistic, as              
s1 =    20          
s2 =    15          
              
Thus, F = s1^2/s2^2 =    1.777777778          

As F < 1.901, then we FAIL TO REJECT HO.

There is no significant evidence that the true standard deviation of the ADD group is greater than the control group at 0.05 level. [CONCLUSION]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.