Question

A researcher wonders whether the recession has changed apartment prices in his city. Before the recession, the mean was known to be $780. He randomly selects 16 apartments. His sample has a mean of $850 and a standard deviation of $75. (a) Test the claim that the price has changed at the =.1 level (b) In addition to your conclusion, write a sentence on whether you would recommend conducting a larger study.

Answer 1

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   780  
Ha:    u   =/   780  
              
As we can see, this is a two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    15          
tcrit =    +/-   1.753
              
Getting the test statistic, as              
              
X = sample mean =    850          
uo = hypothesized mean =    780          
n = sample size =    16          
s = standard deviation = 75
              
Thus, t = (X - uo) * sqrt(n) / s = 3.7333   
              
Also, the p value is      
The two-tailed P value equals 0.0020          
              
As P < 0.10, we   REJECT THE NULL HYPOTHESIS.      

There is significant evidence that the mean apartment price has changed. [CONCLUSION]

b)

As the null hypothesis is rejected at a small sample size, then this may be enough to some practical extent. However, if there is a need to examine the change in price more precisely, then that's where we might want to conduct a larger study.