We are interested in testing a hypothesis regarding the pric

We are interested in testing a hypothesis regarding the price of the concert tickets in the state of Michigan. A random sample of 20 tickets was drawn from a normal population. The mean and standard deviation of the ticket prices in the sample were $120 and $25, respectively. Test the hypothesis Ho: Mu = 125 vs Ha: Mu less than 125 at the 1% significance level.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   125  
Ha:    u   <   125  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    19          
tcrit =    -   2.539483191      
              
Getting the test statistic, as              
              
X = sample mean =    120          
uo = hypothesized mean =    125          
n = sample size =    20          
s = standard deviation =    25          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.894427191          
              
Also, the p value is              
              
p =    0.191142068          
              
As |t| < 2.539, and P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Thus, there is no significant evidence that the mean is less than 125. [CONCLUSION]