Question

16. Real estate broker Elaine Snyderman took a random sample of 12 homes in a prestigious Chicago suburb and found that the average market value Estimate was $ 780,000, with a standard deviation of S 49,000. Test the hypothesis that for all houses in the area, the median estimated value is S 825,000, an alterative hypothesis that it is less than $ 825,000. Use the 0.05 significance level.

I need the answers with all steps and formulas.

Answer 1

Ho :   µ =   825000  
Ha :   µ <   825000   (Left tail test)
          
Level of Significance ,    α =    0.050  
sample std dev ,    s =    49000.0000  
Sample Size ,   n =    12  
Sample Mean,    x̅ =   780000.0000  
          
degree of freedom=   DF=n-1=   11  
          
Standard Error , SE = s/√n =   49000/√12=   14145.0816  
t-test statistic= (x̅ - µ )/SE =    (780000-825000)/14145.0816=   -3.181  
          

          
p-Value   =   0.0044   [Excel formula =t.dist(t-stat,df) ]
Decision:   p-value≤α, Reject null hypothesis       
there is sufficient evidenc eto say that mean is less than 825000

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