The mean age of De Anza College students in a previous term

The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   26.6  
Ha:    u   >   26.6  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    29.4          
uo = hypothesized mean =    26.6          
n = sample size =    56          
s = standard deviation =    2.1          
              
Thus, z = (X - uo) * sqrt(n) / s =    9.977753031          
              
Also, the p value is              
              
p =    9.53686E-24          
              
As P is very very small (Close to 0), we REJECT HO.

There is significant evidence that the mean age for online students is older than 26.6. [ANSWER]