Question

Question 2: A survey is conducted to estimate the average amount spent on utilities for households in a city. 20 clusters are selected by SRSWOR from 60 clusters of the city. Interviewers then obtain the cost of utilities from each household within the sampled clusters; the total costs are shown in the accompany table. \begin{tabular}{|l|c|c|l|c|c|} \hline \begin{tabular}{l} Sampled \\ Cluster \end{tabular} & \begin{tabular}{l} Number of \\ households \end{tabular} & \begin{tabular}{l} Total amount \\ Spent on utilities \end{tabular} & \begin{tabular}{l} Sampled \\ Cluster \end{tabular} & \begin{tabular}{l} Number of \\ households \end{tabular} & \begin{tabular}{l} Total amount \\ Spent on utilities \end{tabular} \\ \hline 1 & 55 & 2210 & 11 & 73 & 2930 \\ \hline 2 & 60 & 2390 & 12 & 64 & 2470 \\ \hline 3 & 63 & 2430 & 13 & 69 & 2830 \\ \hline 4 & 58 & 2380 & 14 & 58 & 2370 \\ \hline 5 & 71 & 2760 & 15 & 63 & 2390 \\ \hline 6 & 78 & 3110 & 16 & 75 & 2870 \\ \hline 7 & 69 & 2780 & 17 & 78 & 3210 \\ \hline 8 & 58 & 2370 & 18 & 51 & 2430 \\ \hline 9 & 52 & 1990 & 19 & 67 & 2730 \\ \hline 10 & 71 & 2810 & 20 & 70 & 2880 \\ \hline \end{tabular} (a) Estimate the average amount a household in the city spends on utilities. (b) Construct a \( 95 \% \) C.I. for the average amount with an unbiased estimate of the variance. (c) Find an unbiased estimate for the total amount spent on utilities of all households in the city. (d) Determine a bound \( B_{a} \) on the absolute error of estimating the total amount with a probability of 0.95 and an unbiased estimate of the variance. (e) Use (d) to construct a \( 95 \% \) C.I. for the total amount. Use \( z_{0.025}=1.96 \) to answer Question 2.

          Question 2:
A survey is conducted to estimate the average amount spent on utilities for households in a city.
20 clusters are selected by SRSWOR from 60 clusters of the city. Interviewers then obtain the cost of utilities from each household within the sampled clusters; the total costs are shown in the accompany table.
\begin{tabular}{|l|c|c|l|c|c|}
\hline \begin{tabular}{l} 
Sampled \\
Cluster
\end{tabular} & \begin{tabular}{l} 
Number of \\
households
\end{tabular} & \begin{tabular}{l} 
Total amount \\
Spent on utilities
\end{tabular} & \begin{tabular}{l} 
Sampled \\
Cluster
\end{tabular} & \begin{tabular}{l} 
Number of \\
households
\end{tabular} & \begin{tabular}{l} 
Total amount \\
Spent on utilities
\end{tabular} \\
\hline 1 & 55 & 2210 & 11 & 73 & 2930 \\
\hline 2 & 60 & 2390 & 12 & 64 & 2470 \\
\hline 3 & 63 & 2430 & 13 & 69 & 2830 \\
\hline 4 & 58 & 2380 & 14 & 58 & 2370 \\
\hline 5 & 71 & 2760 & 15 & 63 & 2390 \\
\hline 6 & 78 & 3110 & 16 & 75 & 2870 \\
\hline 7 & 69 & 2780 & 17 & 78 & 3210 \\
\hline 8 & 58 & 2370 & 18 & 51 & 2430 \\
\hline 9 & 52 & 1990 & 19 & 67 & 2730 \\
\hline 10 & 71 & 2810 & 20 & 70 & 2880 \\
\hline
\end{tabular}
(a) Estimate the average amount a household in the city spends on utilities.
(b) Construct a \( 95 \% \) C.I. for the average amount with an unbiased estimate of the variance.
(c) Find an unbiased estimate for the total amount spent on utilities of all households in the city.
(d) Determine a bound \( B_{a} \) on the absolute error of estimating the total amount with a probability of 0.95 and an unbiased estimate of the variance.
(e) Use (d) to construct a \( 95 \% \) C.I. for the total amount.

Use \( z_{0.025}=1.96 \) to answer Question 2.

Question 2:
A survey is conducted to estimate the average amount spent on utilities for households in a city.
20 clusters are selected by SRSWOR from 60 clusters of the city. Interviewers then obtain the cost of utilities from each household within the sampled clusters; the total costs are shown in the accompany table.

Sampled

Cluster

Number of

households

Total amount

Spent on utilities

Sampled

Cluster

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) Construct a 95 % C.I. for the average amount with an unbiased estimate of the variance.
(c) Find an unbiased estimate for the total amount spent on utilities of all households in the city.
(d) Determine a bound Ba on the absolute error of estimating the total amount with a probability of 0.95 and an unbiased estimate of the variance.
(e) Use (d) to construct a 95 % C.I. for the total amount.

Use z0.025=1.96 to answer Question 2.

Added by Cassandra H.

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