10.42
How long are resale houses on the market? One survey by the Houston Association of Realtors reported that in Houston, resale houses are on the market an average of 112 days. Of course, the length of time varies by market. Suppose random samples of 13 houses in Houston and 11 houses in Chicago that are for resale are traced. The data shown here represent the number of days each house was on the market before being sold. Use the given data and a 1% level of significance to determine whether the population variances for the number of days until resale are different in Houston than in Chicago. Assume the numbers of days resale houses are on the market are normally distributed.
|
Houston |
Chicago |
||
|
132 |
126 |
118 |
56 |
|
138 |
94 |
85 |
69 |
|
131 |
161 |
113 |
67 |
|
127 |
133 |
81 |
54 |
|
99 |
119 |
94 |
137 |
|
126 |
88 |
93 |
|
|
134 |
|
|
|
nH = n1 = 13; Sum of variance for Houston houses:
= 393.3974
nC = n2 = 11; Sum of variance for Chicago houses: 
= 702.6909
H0: 
Ha: 
This is a two-tailed test.
Alpha, α = .01; α/2 = .005
From table A.7, the critical F value for the upper tail is:
The decision rule is to reject the null hypothesis if the observed F value is greater than 5.66.
Compute the sample variances from the given data:
The ratio of sample variances is .5598.
The observed F value is .5598, which is less than the critical value of 5.66. This F-value is in the non-rejection region; therefore we do NOT reject the null hypothesis.
The variances of the two populations are equal.
