Suppose we went to test that the true mean of some variable

Suppose we went to test that the true mean of some variable is equal to 40 against a two- tailed alternative. It is known that the standard deviation of the population is 10. A random sample of 16 observations is drawn from the population and a sample mean is calculated to be 43. Write out the 4 steps of the significance test using a 0.01 level of significance.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   40  
Ha:    u   =/   40  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    15          
tcrit =    +/-   2.946712883      
              
Getting the test statistic, as              
              
X = sample mean =    43          
uo = hypothesized mean =    40          
n = sample size =    16          
s = standard deviation =    10          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.2                  
              
Comparing |t| < 2.9467, WE FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence that the true mean is not 40. [CONCLUSION]