A recent report by the American Medical Association stated t

A recent report by the American Medical Association stated the average annual salary of psychiatrists is $189,121 with a population standard deviation of $26,975. A group of hospital administrators randomly sampled 64 psychiatrists and found an average annual salary of $198,630.   The group claims that the average annual salary is actually higher than what the American Medical Association reported. What is the P-value for this one-sided test? Round to 3 decimal places.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   189121  
Ha:    u   >   189121  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    198630          
uo = hypothesized mean =    189121          
n = sample size =    64          
s = standard deviation =    26975          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.820092678          
              
Thus, the right tailed p value is              
              
p =    0.002400489 = 0.002 [ANSWER]