A psychologist has measured the IQ for a group of 30 childre

A psychologist has measured the IQ for a group of 30 children, now in the third grade, who had been regularly exposed to a new interactive, computerized teaching device. The mean IQ for these children is 106. The mean IQ for the population is 100, with a standard deviation of 16. (6 pts) Test the hypothesis that this group of children are no different from the general population of third graders using alpha = .01. Please provide specific details for all the steps of hypothesis testing.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   100  
Ha:    u   =/   100  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha/2 =    0.005          
zcrit =    +/-   2.575829304      
              
Getting the test statistic, as              
              
X = sample mean =    106          
uo = hypothesized mean =    100          
n = sample size =    30          
s = standard deviation =    16          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.053959591          
              
Also, the p value is              
              
p =    0.039979603          
              
As |z| < 2.576, and P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidence that this group of children are different from the general population of third graders using alpha = .01.       [CONCLUSION]