A random sample of 25 observation from a population produces

A random sample of 25 observation from a population produces a sample mean 20 and variance 25. Find the p-value and test the the hypothesis that the mean is not equal to 22 at a = 0.01

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   22  
Ha:    u   =/   22  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    24          
tcrit =    +/-   2.796939505      
              
Getting the test statistic, as              
              
X = sample mean =    20          
uo = hypothesized mean =    22          
n = sample size =    25          
s = standard deviation =    5          
              
Thus, t = (X - uo) * sqrt(n) / s =    -2          
              
Also, the p value is              
              
p =    0.05693985   [ANSWER, P VALUE]

As P > 0.01, we FAIL TO REJECT THE NULL HYPOTHESIS.  

Hence, there is no significant evidence at 0.01 level that the mean is not equal to 22. [CONCLUSION]