The government of an impoverished country reports the mean a

The government of an impoverished country reports the mean age at death among those who have survived to adulthood as 66.2 years. A relief agency examines 30 randomly selected deaths and obtains a mean of 62.3 years with standard deviation 8.1 years. Test whether the agency’s data support the alternative hypothesis, at the 1% level of significance, that the population mean is less than 66.2.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   66.2  
Ha:    u   <   66.2  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    -   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    62.3          
uo = hypothesized mean =    66.2          
n = sample size =    30          
s = standard deviation =    8.1          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.637182684          
              
Also, the p value is              
              
p =    0.00417989          
              
Comparing |z| > 2.326, (or, p < 0.01), we   REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence that population mean is less than 66.2. [CONCLUSION]