Are the following computer monitors in average the same pric

Are the following computer monitors in average the same price? Test at =.05 significance level. Happy Screens: Average price = $499; standard deviation = $75; n = 40 Great View: Average price = $529; standard deviation = $50; n = 50

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  

At level of significance =    0.05          

As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    499          
X2 =    529          
              
Calculating the standard deviations of each group,              
              
s1 =    75          
s2 =    50          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    40          
n2 = sample size of group 2 =    50          
  
Also, sD =    13.80670127          
              
Thus, the z statistic will be              
              
z = [X1 - X2 - uD]/sD =    -2.172857905          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   1.96
              
              
Also, using p values,              
              
p =    0.029791
              
As |z| > 1.96, and P < 0.05,    WE REJECT THE NULL HYPOTHESIS.          

Thus, there is significant difference between the mean price of computer monitors in Happy Screens and Great View at 0.05 level. [CONCLUSION]