Consider the following hypothesis test Ho u 15 Ha u 15 A s

Consider the following hypothesis test: Ho: u = 15, Ha: u = 15 A sample of 50 provided a sample mean of 14.5. The population standard deviation is 3. A. Compute the value of the test statistic. B. what is the p-value. C. Using a = 0.05, what is your conclusion

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   15  
Ha:    u   =/   15  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha/2 =    0.025          
zcrit =    +/-   1.959963985      
              
Getting the test statistic, as              
              
X = sample mean =    14.5          
uo = hypothesized mean =    15          
n = sample size =    50          
s = standard deviation =    3          
              
Thus, z = (X - uo) * sqrt(n) / s =    -1.178511302 [ANSWER, TEST STATISTIC]

**************************

b)          
              
Also, the p value is, as this is two tailed,              
              
p =    0.238592829   [ANSWER]
************************

c)      
              
As P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidnece at 0.05 level that the mean is not equal to 15. [ANSWER]