Question

A government agency reported in a comprehensive​ survey, released every three​ years, that the average income of families in the country declined from 2001 to 2004. This was the first decline since​ 1989-1992. A sample of incomes was taken in 2001 and repeated in 2004. After adjusting for​ inflation, the data that arise from these samples are given in the accompanying table. Complete parts a through d below.

Income01	Income04
89674	74294
55820	84415
62416	82420
58801	94178
64470	66761
58365	88383
75058	81270
79473	52612
75508	57955
65224	66832
47786	81388
85034	42372
94578	47724
80254	71969
75258	74927
74325	34608
62403	90584
68417	94941
75215	56950
57909	80871
57858	74940
90228	68894
101609	86595
78658	78321
76120	64536
65351	67254
82719	63616
55289	61692
87498	69186
57392	72701
69421	74133
68963	72267
73772	69406
54029	47265
64984	94891
71916	93104
68184	64834
71472	83586
77660	82507
49095	76474
86992	74443
84163	67876
65455	50284
74978	83693
82558	55851
96091	78123
71743	64450
67653	92486
87078	76795
72570	86684

a. Determine the percentage decline indicated by the two samples.

The percentage decline is _______​%. ​(Round to two decimal places as​ needed.)

b. Using these​ samples, produce a 90​% confidence interval for the difference in the average family income between 2001 and 2004.

The 90​% confidence interval is _________less than or equals​(mu 1minusmu 2​)less than or equals

____________.

​(Round to two decimal places as​ needed.)

c. Is it plausible that there as been no decline in the average income of​ families? Support your assertion.

A.

No​, because the interval contains the value 0.

B.

Yes​, because the interval does not contain the value 0.

C.

No​, because the interval does not contain the value 0.

D.

Yes​, because the interval contains the value 0.

d. How large an error could you have made by using the difference in the sample means to estimate the difference in the population​ means?

The error could have been as large as

nothing.

​(Round to the nearest whole number as​ needed.)

Answer 1

	Income(01)	Income(04)
Total	3617487	3622341
Decline=	4854
Percentage decline=	0.1342
Average(01)=	72349.74
Average(04)=	72446.82
Sample variance(01)=	154120335.1
Sample variance(04)=	203228907.3
S(01)=	12414.52114
S(04)=	14255.83766

Percentage decline=0.13%

c. Is it plausible that there as been no decline in the average income of​ families? Support your assertion.

D.

Yes​, because the interval contains the value 0.

SE=

=2673.38=2673