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.