(b) In the region, houses are considered large if they are greater than 2,500 square feet and expensive if the selling price is greater than $300,000. The following two-way table summarizes the houses in the sample. Large Not Large Total Expensive 8 2 10 Not Expensive 4 16 20 Total 12 18 30 (i) Use the information in the table to construct a graphical display of the data. (ii) Assume there is no association between size (large, not large) and price (expensive, not expensive). Use the given totals to complete the following table with the expected number of houses for each classification if there was no association. Large Not Large Total Expensive 10 Not Expensive 20 Total 12 18 30
(b) In the region, houses are considered large if they are greater than 2,500 square feet and expensive if the selling price is greater than $300,000. The following two-way table summarizes the houses in the sample.
| Large | Not Large | Total | |
| Expensive | 8 | 2 | 10 |
| Not Expensive | 4 | 16 | 20 |
| Total | 12 | 18 | 30 |
(i) Use the information in the table to construct a graphical display of the data.
(ii) Assume there is no association between size (large, not large) and price (expensive, not expensive). Use the given totals to complete the following table with the expected number of houses for each classification if there was no association.
| Large | Not Large | Total | |
| Expensive | 10 | ||
| Not Expensive | 20 | ||
| Total | 12 | 18 | 30 |
For associations displayed in the scatterplot, the strength of linear association is measured by the correlation coefficient . For the scatterplot of houses, r=0.82. For associations that are summarized in two-way tables, the strength of association is measured by the chi-square statistic. The formula for the chi-square statistic is χ2=Σ(observed−expected)2expected, where expected is the count assuming no association and observed is the count shown by the data. Greater values of χ2 indicate stronger association. For the table of counts in part (b), χ2=10.
(c) Suppose the selling price for the most expensive house in the sample is decreased from $489,000 to $325,000.
(i) What effect would the decrease have on the value of r? Explain your reasoning.
(ii) What effect would the decrease have on the value of χ2? Explain your reasoning.
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