In: Statistics and Probability
14. BigDeal Real Estate surveyed prices per square foot in the valley and foothills of Hoke-a-mo, Utah. Based on BD’s DATA link, prices per square foot equal at α = 0.01?
a. The critical value is 2.977 since this is a two-tail scenario. The test statistic is 1.936. Since the test statistic < the critical value, the test statistic does not lie in the area of rejection. Do not reject the null hypothesis. The prices per square foot are equal at alpha = 0.01.
b. The critical value is 2.977 since this is a two-tail scenario. The test statistic is 2.239. Since the test statistic < the critical value, the test statistic does not lie in the area of rejection. Do not reject the null hypothesis. The prices per square foot are equal at alpha = 0.01.
c. The critical value is 2.977 since this is a two-tail scenario. The test statistic is 1.513. Since the test statistic < the critical value, the test statistic does not lie in the area of rejection. Do not reject the null hypothesis. The prices per square foot are equal at alpha = 0.01.
d. The critical value is 2.977 since this is a two-tail scenario. The test statistic is 3.207. Since the test statistic > the critical value, the test statistic does lie in the area of rejection. Reject the null hypothesis. The prices per square foot are not equal at alpha = 0.01.
| Valley | Foothills | 
| 109 | 82 | 
| 116 | 161 | 
| 106 | 163 | 
| 157 | 112 | 
| 147 | 222 | 
| 105 | 137 | 
| 173 | 226 | 
| 153 | 200 | 
| 137 | 154 | 
| 110 | 176 | 
Sample #1   ---->   1  
           
   
mean of sample 1,    x̅1=   131.300  
           
   
standard deviation of sample 1,   s1 =   
25.091          
       
size of sample 1,    n1=   10  
           
   
          
           
   
Sample #2   ---->   2  
           
   
mean of sample 2,    x̅2=   163.300  
           
   
standard deviation of sample 2,   s2 =   
45.838          
       
size of sample 2,    n2=   10  
           
   
          
           
   
difference in sample means =    x̅1-x̅2 =   
131.3000   -   163.3   =  
-32.000  
          
           
   
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 -
1)s2²]/(n1+n2-2)) =    36.9506  
           
   
std error , SE =    Sp*√(1/n1+1/n2) =   
16.5248          
       
          
           
   
t-statistic = ((x̅1-x̅2)-µd)/SE = (  
-32.0000   -   0   ) /   
16.52   =   -1.936
a. The critical value is 2.977 since this is a two-tail scenario. The test statistic is 1.936. Since the test statistic < the critical value, the test statistic does not lie in the area of rejection. Do not reject the null hypothesis. The prices per square foot are equal at alpha = 0.01.