8.10 An economic survey is designed to estimate the average amount spent on utilities for households in a city. Because no list of households is available, cluster sampling is used, with divisions (wards) forming the clusters. A simple random sample of 20 wards is se- lected from the 60 wards of the city. Interviewers then obtain the cost of utilities from each household within the sampled wards; the total costs are shown in the accompanying table. Estimate the average amount a household in the city spends on utilities and place a bound on the error of estimation. Total amount Total amount spent on utilities spent on utilities Sampled Number of Number of Sampled ward ward households (dollars) households (dollars) 1 55 2210 11 73 2930 2 60 2390 12 64 2470 3 63 2430 13 69 2830 4 58 2380 14 58 2370 5 71 2760 15 63 2390 78 3110 16 75 2870 7 69 2780 17 78 3210 8. 58 2370 18 51 2430 9. 52 1990 19 67 2730 10 71 2810 20 70 2880

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8.10 An economic survey is designed to estimate the average amount spent on utilities for
households in a city. Because no list of households is available, cluster sampling is used,
with divisions (wards) forming the clusters. A simple random sample of 20 wards is se-
lected from the 60 wards of the city. Interviewers then obtain the cost of utilities from
each household within the sampled wards; the total costs are shown in the accompanying
table. Estimate the average amount a household in the city spends on utilities and place
a bound on the error of estimation.
Total amount
Total amount
spent on
utilities
spent on
utilities
Sampled
Number of
Number of
Sampled
ward
ward
households
(dollars)
households
(dollars)
1
55
2210
11
73
2930
2
60
2390
12
64
2470
3
63
2430
13
69
2830
4
58
2380
14
58
2370
5
71
2760
15
63
2390
78
3110
16
75
2870
7
69
2780
17
78
3210
8.
58
2370
18
51
2430
9.
52
1990
19
67
2730
10
71
2810
20
70
2880
Transcribed Image Text:8.10 An economic survey is designed to estimate the average amount spent on utilities for households in a city. Because no list of households is available, cluster sampling is used, with divisions (wards) forming the clusters. A simple random sample of 20 wards is se- lected from the 60 wards of the city. Interviewers then obtain the cost of utilities from each household within the sampled wards; the total costs are shown in the accompanying table. Estimate the average amount a household in the city spends on utilities and place a bound on the error of estimation. Total amount Total amount spent on utilities spent on utilities Sampled Number of Number of Sampled ward ward households (dollars) households (dollars) 1 55 2210 11 73 2930 2 60 2390 12 64 2470 3 63 2430 13 69 2830 4 58 2380 14 58 2370 5 71 2760 15 63 2390 78 3110 16 75 2870 7 69 2780 17 78 3210 8. 58 2370 18 51 2430 9. 52 1990 19 67 2730 10 71 2810 20 70 2880
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