4. 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 used, with divisions (wards) forming the clusters. A simple random sample of 20 wards is selected from 60 wards of city. Interviewers then obtain the cost of utilities from each household within the sampled wards; the total costs are shown in accompanying table. Total Total amount amount Sampled ward Number of spent on Sampled Number of households utilities ($) ward households spent on utilities ($) 1 55 2210 11 73 2930 123456789 60 2390 12 64 2470 63 2430 13 69 2830 58 2380 14 58 2370 71 2760 15 63 2390 78 3110 16 75 2870 69 2780 17 78 3210 58 2370 18 51 2430 52 1990 19 67 2730 10 71 2810 20 70 2880 a. Estimate the average amount a household in the city spends on utilities, and place a bound on the error of estimation. b. In survey, the number of households in the city is not known. Estimate the total amount spent on utilities for all households in the city and place a bound on the error of estimation.
4. 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 used, with divisions (wards) forming the clusters. A simple random sample of 20 wards is selected from 60 wards of city. Interviewers then obtain the cost of utilities from each household within the sampled wards; the total costs are shown in accompanying table. Total Total amount amount Sampled ward Number of spent on Sampled Number of households utilities ($) ward households spent on utilities ($) 1 55 2210 11 73 2930 123456789 60 2390 12 64 2470 63 2430 13 69 2830 58 2380 14 58 2370 71 2760 15 63 2390 78 3110 16 75 2870 69 2780 17 78 3210 58 2370 18 51 2430 52 1990 19 67 2730 10 71 2810 20 70 2880 a. Estimate the average amount a household in the city spends on utilities, and place a bound on the error of estimation. b. In survey, the number of households in the city is not known. Estimate the total amount spent on utilities for all households in the city and place a bound on the error of estimation.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Question
Transcribed Image Text:4. 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
used, with divisions (wards) forming the clusters. A simple random sample of 20
wards is selected from 60 wards of city. Interviewers then obtain the cost of utilities
from each household within the sampled wards; the total costs are shown in
accompanying table.
Total
amount
Total
amount
Sampled Number of
spent on
Sampled
Number of
ward
households
utilities ($)
ward
households
spent on
utilities ($)
1
55
2210
11
73
2930
234567890
60
2390
12
64
2470
63
2430
13
69
2830
58
2380
14
58
2370
71
2760
15
63
2390
78
3110
16
75
2870
69
2780
17
78
3210
58
2370
18
51
2430
52
1990
19
67
2730
10
71
2810
20
70
2880
a. Estimate the average amount a household in the city spends on utilities, and
place a bound on the error of estimation.
b. In survey, the number of households in the city is not known. Estimate the
total amount spent on utilities for all households in the city and place a bound
on the error of estimation.
Transcribed Image Text:c. The economic survey is to be performed in a neighboring city of similar
structure. The objective is to estimate the total amount spent on utilities by
households in the city, with a bound of $5000 on the error of estimation. Use
the data above to find the appropriate number of clusters needed to achieve
this bound.
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Step 1: Write the given information.
VIEWStep 2: Compute the average amount a household in the city spends on utilities.
VIEWStep 3: Compute the standard deviation and bound on the error of estimation.
VIEWStep 4: Compute total amount spent on utilities for all households and place a bound on error of estimation.
VIEWStep 5: Compute the minimum number of clusters required to achieve the given bound.
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