The amount of income spent on housing is an important component of the cost of l
ID: 3436643 • Letter: T
Question
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, 5 years ago and now. The information is reported below. Is it reasonable to conclude the percent is less now than 5 years ago?
Homeowner FiveYears
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
Explanation / Answer
Mean x =6.35
Std Deviation s = 12.4778
H0: Difference = 0
H1: D > 0
= 0.05
degree of freedom = n-1 = 20-1 = 19
Critical value = T from table 2 – t distribution when v=0.05 and n= 19 = 1.729
Test statistic T = (mean-0)/(std deviation / n)
(6.35 -0) / (12.4778 / 20) = 2.2759
Conclusion: Since 2.2759 > 1.729, we conclude that the percentage is less now than it was 5 years ago.
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