Question 1 The dean of a large college is concerned that the

Question
1. The dean of a large college is concerned that the students grade-point averages have changed dramatically in recent years. The graduating seniors mean GPA over the past 5 years is 2.95. The dean randomly samples 30 seniors from the last graduating class and finds that their mean GPA is 2.75, with a standard deviation of 0.75. Test the null hypothesis that the mean GPA for the graduating seniors is 2.95 (i.e., H0: m = 2.75).

Solution

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   2.95  
Ha:    u   =/   2.95  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    2.75          
uo = hypothesized mean =    2.95          
n = sample size =    30          
s = standard deviation =    0.75          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.460593487          
              
Also, the p value is              
              
p =    0.144127035          

This P value is big, and is greater than 0.10 (the highest usual significance level).
              
As P is large (> 0.10), we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidence that he students\' grade-point averages have changed dramatically in recent years.   [CONCLUSION]