Question

1. Thirty GPAs from a randomly selected sample of statistics students at a college reported a mean of 3.11 and the standard deviation was 0.36. Assume that the population distribution is approximately Normal. The technician in charge of records claimed that the population mean GPA for the whole college is 2.88. The chair of the mathematics department claims that students typically have higher GPAs than the typical college student. Test this claim.
   1. State the null and alternative hypotheses
   2. Find the test statistic t.
   3. Find the p-value.
   4. Do you reject or not reject the null hypothesis?
   5. What can you conclude about the mean GPA for statistic students?

Answer 1

a)

Null hypothesis     

           
                  
Alternative hypothesis      

b)
                  
We have for given sample,                  
Population mean for given sample=2.88  
Sample mean=3.11          
Sample standard deviation s=0.36      
Sample size =n=   30          
                  
Degree of freedom = n-1 =29      
                  
t critical value by using (t table)=1.833      
                  
t test statistic formula is


=3.50

c) P value is 0.0008.................by using Excel command TDIST(3.50,29, 1)

d) P value is 0.0008 < 0.01

Therefore, we reject H0.

e) Conclusion: We have sufficient evidence at to say that,  students typically have higher GPAs than the typical college student.