Use hypothesis tests seven step method to answer the followi

Use hypothesis tests seven step method to answer the following.  

Researchers collected a simple random sample of the times that 81 college students required to earn their bachelor\'s degrees. The sample has a mean of 4.8 years and a standard deviation of 2.2 years (based on data from the National Center for Education Statistics). Use a 0.05 significance level to test the claim that the mean time for all college students is greater than 4.5 years

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   4.5  
Ha:    u   >   4.5  
              
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 =    4.8          
uo = hypothesized mean =    4.5          
n = sample size =    81          
s = standard deviation =    2.2          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.227272727          
              
Also, the p value is              
              
p =    0.109860051          
              
Comparing z < 1.64485, (or, P > 0.05), we   FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that the mean time for all college students to earn their bachelor\'s degrees is greater than 4.5 years. [CONCLUSION]