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3. An economic survey is designed to estimate the average amount spent on utilities for households in a city. Since no list of households is available, cluster sampling is used, with wards forming the clusters. A simple random sample of 20 wards is selected 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. Sampled ward | Number of households | Total amount ($) spent on utilities | Sampled ward | Number of households | Total amount ($) spent on utilities 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 6 | 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 a. Estimate the average amount a household in the city spends on utilities. b. Find the variance. c. Although the number of households in the city is unknown. Estimate the total amount spent on utilities for all households in the city. d. Find the variance.

          3. An economic survey is designed to estimate the average amount spent on utilities for households in a city. Since no list of households is available, cluster sampling is used, with wards forming the clusters. A simple random sample of 20 wards is selected 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.

Sampled ward | Number of households | Total amount ($) spent on utilities | Sampled ward | Number of households | Total amount ($) spent on utilities
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
6 | 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

a. Estimate the average amount a household in the city spends on utilities.
b. Find the variance.
c. Although the number of households in the city is unknown. Estimate the total amount spent on utilities for all households in the city.
d. Find the variance.

3. An economic survey is designed to estimate the average amount spent on utilities for households in a city. Since no list of households is available, cluster sampling is used, with wards forming the clusters. A simple random sample of 20 wards is selected 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.

Sampled ward | Number of households | Total amount () spent on utilities | Sampled ward | Number of households | Total amount () spent on utilities
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
6 | 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

a. Estimate the average amount a household in the city spends on utilities.
b. Find the variance.
c. Although the number of households in the city is unknown. Estimate the total amount spent on utilities for all households in the city.
d. Find the variance.

Added by Bryan W.

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