A state executive claims that the average number of acres in

A state executive claims that the average number of acres in western PA state park is less than 2000 acres. A random sample of five parks is selected and the number of acres is given below. With ? = 0.02 is there enough evidence to support the claim? 959, 1187, 493, 6249, 541

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   2000  
Ha:    u   <   2000  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    4          
tcrit =    -   2.998527873      
              
Getting the test statistic, as              
              
X = sample mean =    1885.8          
uo = hypothesized mean =    2000          
n = sample size =    5          
s = standard deviation =    2456.276287          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.103961824          
              
As |t| < 2.9985, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence that the average number of acres in western PA state park is less than 2000 acres. [CONCLUSION]