A newspaper in a large midwestern city reported that the Nat

A newspaper in a large midwestern city reported that the National Association of Realtors said that the mean home price last year was $116,800. The city housing department feels that this figure is too low. They randomly selected 56 home sales and the sample mean is $118,000 and the sample standard deviation is $3,700. Conduct hypothesis test using a=.01. Use traditional and p-value approach to hypothesis testing. Show all of the steps for each approach.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   116800  
Ha:    u   >   116800  
              
As we can see, this is a    right   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 =    118000          
uo = hypothesized mean =    116800          
n = sample size =    56          
s = standard deviation =    3700          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.427021008  
As z > 2.326, we REJECT THE NULL HYPOTHESIS.      
              
Also, the p value is              
              
p =    0.007611687          
              
As p < 0.01,   REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that the mean home price is greater than $116,800. [CONCLUSION]