in national use a vocabulary test is known to have a mean sc

in national use, a vocabulary test is known to have a mean score of 68 and a standard deviation of 13. A class of 19 students takes the test and has a mean score of 65. is this class significantly worse than the average of those who have taken the test ?

Solution

As the significance level is not given, we assume it is 0.05.

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   68  
Ha:    u   <   68  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    18          
tcrit =    -   1.734063607      
              
Getting the test statistic, as              
              
X = sample mean =    65          
uo = hypothesized mean =    68          
n = sample size =    19          
s = standard deviation =    13          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.005899756          
              
Also, the p value is              
              
p =    0.163897745          
              
As |t| < 1.734, and P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, this class IS NOT significantly worse than the average of those who have taken the test. [CONCLUSION]

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