107 116 92 109 114 95 102 125 118117 63 114 90 77 83 116 44

10.7, 11.6, 9.2, 10.9, 11.4, 9.5, 10.2, 12.5, 11.8,11.7, 6.3, 11.4, 9.0, 7.7, 8.3

11.6, 4.4, 10.2, 8.5, 8.8, 10.6, 10.3, 4.7, 13.1, 13.3,9.7, 11.5, 9.2, 11.3, 7.0

Perform a one-tailed test.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

According to a high-profile realtor, houses in the sleepy town of Sun Beach have shown higher appreciation over the past three years than have houses in the bustling town of North Arden. To test the realtor\'s claim, an economist has found fifteen recently sold homes in Sun Beach and fifteen recently sold homes in North Arden that were owned for exactly three years. The following table gives the appreciation (expressed as a percentage increase) for each of the thirty houses. Appreciation rates in percent Sun Beach 10.7, 11.6, 9.2, 10.9, 11.4, 9.5, 10.2, 12.5, 11.8,11.7, 6.3, 11.4, 9.0, 7.7, 8.3 North Arden 11.6, 4.4, 10.2, 8.5, 8.8, 10.6, 10.3, 4.7, 13.1, 13.3,9.7, 11.5, 9.2, 11.3, 7.0 Assume that the two populations of appreciation rates are normally distributed and that the population variances are equal. Can we conclude, at the level of significance, that houses in Sun Beach have higher appreciation over the past three years than houses in North Arden? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Solution

a)

Let

u1 = mean of sun beach
u2 = mean of north arden

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
H1:   u1 - u2   >   0   [ANSWER]

****************

b)

t [ANSWER, TYPE OF TEST STATISTIC]

****************

C)

At level of significance =    0.05          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    10.14666667          
X2 =    9.613333333          
              
Calculating the standard deviations of each group,              
              
s1 =    1.765489275          
s2 =    2.647334688          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    15   , n2 =    15  
              
Then              
              
S =    2.250037037          
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    0.82159736          
              
As ud = the hypothesized difference between means =    0   , then      
              
t = [X1 - X2 - ud]/Sd =    0.649141975   [ANSWER, TEST STATISTIC]

*******************

d)      
              
          
df = n1 + n2 - 2 =    28          
              
Getting the p value using technology,              
              
p =    0.26076808   [ANSWER, P VALUE]

************************
      
NO. We cannot conclude that houses in Sun Beach have higher appreciation. [ANSWER, NO]

*****************************************************

Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!