Carry out a hypothesis test for the conditions laid out in e

Carry out a hypothesis test for the conditions laid out in exercise 7 (copied below) for an observed X of 46.5. Is this statistically significant at alpha= 0.05?

(7: \"In exercise 3 you tested Ho:u=50 based on a sample of n=36 showing x=48.8. The population had a standard deviation of 7.5.)

Solution

Formulating the null and alternative hypotheses,          
          
Ho:   u   =   50
Ha:    u   =/   50
          
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 =    46.5      
uo = hypothesized mean =    50      
n = sample size =    36      
s = standard deviation =    7.5      
          
Thus, z = (X - uo) * sqrt(n) / s =    -2.8      
          
Also, the p value is          
          
p =    0.005110261      
          
Comparing z and zcrit (or p < 0.05), we   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that the mean is not 50. [CONCLUSION]