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 18 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 H_0: 125 vs. H_a

Solution

16.

Here, we use t as n < 30.

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 =    17          
tcrit =    -   2.566933984      
              
Getting the test statistic, as              
              
X = sample mean =    120          
uo = hypothesized mean =    125          
n = sample size =    18          
s = standard deviation =    25          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.848528137 = -0.85          
              
As |t| < 2.5669, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no sufficient evidnece to reject Ho.

So,

OPTION A: t = -0.85, NO [ANSWER]