A random sample of 16 clients records from a large super mar

A random sample of 16 client\'s records from a large super market membership was taken. Sample shows the average age was 78.6 years with a st. d. of 8 years. We are interested in determining whether the average age of the population is significantly more than 75 years. Assume the distribution of the population of ages is normal. At 95% confidence, it can be concluded that the average age of the population

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   75  
Ha:    u   >   75  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    15          
tcrit =    +   1.753050356      
              
Getting the test statistic, as              
              
X = sample mean =    78.6          
uo = hypothesized mean =    75          
n = sample size =    16          
s = standard deviation =    8          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.8          
              
Also, the p value is              
              
p =    0.046001059          
              
As |t| > 1.753, or P < 0.05, we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the average age of the population is significantly more than 75 years. [CONCLUSION]