45 people are randomly selected and the accuracy of their wr

45 people are randomly selected and the accuracy of their wristwatches is checked. with positive errors representing watches that are ahead of the correct time and negative errors representing watches that are behind the correct time. The 45 values have a mean of 91sec and a standard deviation of 242sec. Use a 0.01 significance level to test the claim that the population of all watches has a mean of 0 sec.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   0  
Ha:    u   =/   0  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha/2 =    0.005          
zcrit =    +/-   2.575829304      
              
Getting the test statistic, as              
              
X = sample mean =    91          
uo = hypothesized mean =    0          
n = sample size =    45          
s = standard deviation =    242          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.522506437          
              
Also, the p value is              
              
p =    0.011652182          
              
Comparing |z| < 2.5758, (or, p > 0.01), we   FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Thus, there is no significant evidence that the mean is not 0 sec. [CONCLUSION]