The College Entrance Exam Board states that the mean score o

The College Entrance Exam Board states that the mean score on the achievement test they administer is 450 with a standard deviation of 40. After tutoring a group of 100 students, you test the students and their mean is 464. Do a hypothesis test to find if the sample mean is significantly higher than the mean claimed by the CEEB. Use = .03 and the prob-value approach.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   450  
Ha:    u   >   450  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    464          
uo = hypothesized mean =    450          
n = sample size =    100          
s = standard deviation =    40          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.5          
              
Also, the p value is              
              
p =    0.000232629          
              
As P < 0.03, we   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that this sample came from a population with significantly higher population mean than the mean claimed by the CEEB. [CONCLUSION]