at < 30,000 income 30% own homes and 70% rent

at > 80,000 income 70% own homes and 30% rent

Thus we can take our sample and find that

at < 30,000 income 40% own homes and 60% rent

at > 80,000 income 60% own homes and 40% rent

To find our test statistic we take the sum of the actual value from the expected, divided by the expected.

sum across i and sum across j (n

_{ij}- e

_{ij})

^{2}/ e

_{ij}

We use the resultant test statistic and find where it falls on the x-axis of a chi-square distribution. If it falls so that the area to the right and the area above the point is sufficiently less than 0.05 (or our probability tolerance) we assume the data is homogeneous.

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