## Question 875:

1## Answer:

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Here we need to compare the means of two groups. However, we have the same 20 homeowners in both before and after groups. When we have the same people in both groups and want to compare the difference we use the paired-t test (also called match t-test). In fact, we could also just subtract the differences for each homeowner and use a 1-sample t-test on these difference scores to see if the difference was not equal to 0.You can use the paired t-test in the Excel Analysis Service Pack by selecting t-test Paired Sample for Means. Put the "five years ago group" in the Variable 1 range and the now group in the Variable 2 range. Put 0 in the Hypothesized Mean difference (since we want to know whether the difference is less now than it was five years ago). This would be a one-tailed test as we want to know whether the mean is less than 0. The Null Hypothesis is the difference is equal to 0. We will reject the Null if the p-value is less than .05.

The difference is 6.3% less now that it was 5 years ago.

The 1-tailed p-value is .0179 (P(T<=t) one-tail) which is less than .05 so we reject the Null. We conclude that housing costs as percent of income has reduced in the last five years.

You can also see more calculations in the attached excel file.