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# Paired t test: Cost of Living

The amount of income spent on housing is an important component of the cost of living. The total costs of housing for homeowners might include mortgage payments, property taxes, and utility costs (water, heat, electricity). An economist selected a sample of 20 homeowners in New England and then calculated these total housing costs as a percent of monthly income, five years ago and now. The information is reported below. Is it reasonable to conclude the percent is less now than five years ago?

Homeowner Five Years Ago Now
1 17% 10%
2 20% 39%
3 29% 37%
4 43% 27%
5 36% 12%
6 43% 41%
7 45% 24%
8 19% 26%
9 49% 28%
10 49% 26%
11 35% 32%
12 16% 32%
13 23% 21%
14 33% 12%
15 44% 40%
16 44% 42%
17 28% 22%
18 29% 19%
19 39% 35%
20 22% 12%

#### Solution Summary

The solution provides step by step method for the calculation of test statistic for a paired t test. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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