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# Hypothesis testing- before and after

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

#### Solution Preview

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?

in % in %
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

Testing differences between means with dependent samples
Since the problem does not specify the level of significance at which the hypothesis is to be tested a value of 10% is assumed.

A) The mean and standard deviation of difference is calculated

Homeowner ...

#### Solution Summary

The hypothesis that total housing costs as a percent of monthly income, is ess now than five years ago has been tested.

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