A state education agency designs and administers high school

A state education agency designs and administers high school proficiency exams. Historically, time to complete the exam was an average of 120 minutes. Recently the format of the exam changed and the claim has been made that the time to complete the exam has changed. A sample of 50 new exam times yielded an average time of 118 minutes. The standard deviation is assumed to be 5 minutes. Calculate the p-value.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   120  
Ha:    u   <   120  
              
As we can see, this is a    2   tailed test.      
              
Getting the test statistic, as              
              
X = sample mean =    118          
uo = hypothesized mean =    120          
n = sample size =    50          
s = standard deviation =    5          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.828427125          
              
Also, the p value is              
              
p =    0.004677735   [ANSWER]