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Value of Owner-Occupied Homes: Problem |
A census study was carried out, in which data was collected from 506 housing tracts in the Boston area. Some of the variables of interest for each tract were median home value, crime rate, relative distance from the Charles River (near or far), percentage of lower economic status families, and so on.
Use a two-sample t-test (with significance level α = 0.05) to determine whether, on average, the median value of owner-occupied homes near the Charles River is greater than that of homes farther away from it.
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SAS Institute Inc.
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Value of Owner-Occupied Homes: Sample Data | |
The Bostonhousing data set contains census information for 506 housing tracts in the Boston area. These are the variables in the data set: Name | Type | Description | | MedianValue | num | median value of owner-occupied homes in $1000's | | Crime | num | per capita crime rate by town | | Zone | num | proportion of residential land zoned for lots over 25,000 sq.ft | | Industry | num | proportion of non-retail business acres per town | | Charles | char | Charles River dummy variable (= 1 if tract bounds river; 0 otherwise) | | NOX | num | nitric oxides concentration (parts per 10 million) | | Rooms | num | average number of rooms per dwelling | | Bef_1940 | num | proportion of owner-occupied units built prior to 1940 | | DistEmp | num | weighted distances to five Boston employment centers | | Highways | num | index of accessibility to highways | | TaxRate | char | full-value property-tax rate per $10,000 | | PTRatio | char | pupil-teacher ratio by town | | LowStatus | char | % lower status of the population | |
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Source of Data
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This data is sample data from SAS Institute Inc. |
Value of Owner-Occupied Homes: Solution |
Looking for evidence that the median home value for homes near the Charles River is greater than that for homes farther away, you test the hypotheses
Ho: μ=0 versus Ha: μ< 0,
where μ is the mean difference in median home value (Far - Near). The median value for houses near the Charles River is 28.44, and the median value for houses farther away is 22.094. The difference is -6.346. Depending on the method you use for the t-test, this difference may or may not be significant. For example, for more accuracy, you can use the Satterthwaite method, which accounts for the possibility of unequal variances between the two populations (which is tested by the F-test). Using the Satterthwaite method, the t statistic has a value of -3.11, which indicates evidence that the median home value for “near homes” is greater than the median home value for “far homes.”
The p-value for a two-sided test is 0.0036. To obtain the p-value for a one-sided test, you divide this by two, which results in an outcome that is still significant at the a = 0.05 level (p-value = 0.0018).
So, you can conclude that on average, the median value of owner-occupied homes near the Charles River is greater than that of owner-occupied homes farther from the river. |
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