The amount of income spent on housing is an important compon

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. An economist selected a sample of 20 homeowners in New England and then calculated 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? Use the 0.05 level of significance. (answers to 3 decimal places)

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

Hint: compute the difference (positive d means costs greater, negative means costs less. You might find it convenient to transcribe the data to a spreadsheet.

Here

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

First from the given data, find mean and std deviation and also xy

  H0:

Homeowner	Five Years Ago (%)	Now (%)
	x	y	xy
1	17	10	170
2	20	39	780
3	29	37	1073
4	43	27	1161
5	36	12	432
6	43	41	1763
7	45	24	1080
8	19	26	494
9	49	28	1372
10	49	26	1274
11	35	32	1120
12	16	32	512
13	23	21	483
14	33	12	396
15	44	40	1760
16	44	42	1848
17	28	22	616
18	29	19	551
19	39	35	1365
20	22	12	264
Mean	33.15	26.85	925.7
Std dev	11.08472159	10.38356495