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to Just 6) A county government is interested in expanding the facilities of a day-care center for mentally disabled children. The expansion will increase the cost of enrolling a child in the center. A sample survey will be conducted to estimate the proportion of families with disabled children that will make use of the expanded facilities. The families are divided into those who use the existing facilities and those who do not. Some families live in the city in which the center is located, and some live in the surrounding suburban and rural areas. Thus, stratified random sampling is used, with users in the city, users in the surrounding country, nonusers in the city, and nonusers in the country forming strata 1, 2, 3, and 4, respectively. Approximately 90% of the present users and 50% of the present nonusers will use the expanded facilities. The cost of obtaining an observation from a user is $3 and from nonuser is $7. The difference in cost results because nonusers are difficult to locate. a) Existing records give N₁ = 107, N₂ = 50, №3 = 152 and N4 = 68. Find the approximate sample size and allocation necessary to estimate the population proportion with a bound of 5% on the error of estimation. b) Suppose for the sample data captured after this survey was conducted yielded the following proportion of families who will use the new facilities: ₁ = .86,₂ = .94,3 = .65 and 4 = .55 Estimate the population proportion p, and place a bound on the error of estimation. Was the desired bound achieved? * c) Suppose that the total cost of sampling is fixed at $600. Choose the sample size and allocation that minimiz.es the variance of the estimator pst for this fixed cost.

to Just 6) A county government is interested in expanding the facilities of a day-care center for mentally disabled children. The expansion will increase the cost of enrolling a child in the center. A sample survey will be conducted to estimate the proportion of families with disabled children that will make use of the expanded facilities. The families are divided into those who use the existing facilities and those who do not. Some families live in the city in which the center is located, and some live in the surrounding suburban and rural areas. Thus, stratified random sampling is used, with users in the city, users in the surrounding country, nonusers in the city, and nonusers in the country forming strata 1, 2, 3, and 4, respectively. Approximately 90% of the present users and 50% of the present nonusers will use the expanded facilities. The cost of obtaining an observation from a user is $3 and from nonuser is $7. The difference in cost results because nonusers are difficult to locate. a) Existing records give N₁ = 107, N₂ = 50, №3 = 152 and N4 = 68. Find the approximate sample size and allocation necessary to estimate the population proportion with a bound of 5% on the error of estimation. b) Suppose for the sample data captured after this survey was conducted yielded the following proportion of families who will use the new facilities: ₁ = .86,₂ = .94,3 = .65 and 4 = .55 Estimate the population proportion p, and place a bound on the error of estimation. Was the desired bound achieved? * c) Suppose that the total cost of sampling is fixed at $600. Choose the sample size and allocation that minimiz.es the variance of the estimator pst for this fixed cost.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 28PPS
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to Just 6) A county government is interested in expanding the facilities of a day-care center for mentally disabled children. The expansion will increase the cost of enrolling a child in the center. A sample survey will be conducted to estimate the proportion of families with disabled children that will make use of the expanded facilities. The families are divided into those who use the existing facilities and those who do not. Some families live in the city in which the center is located, and some live in the surrounding suburban and rural areas. Thus, stratified random sampling is used, with users in the city, users in the surrounding country, nonusers in the city, and nonusers in the country forming strata 1, 2, 3, and 4, respectively. Approximately 90% of the present users and 50% of the present nonusers will use the expanded facilities. The cost of obtaining an observation from a user is $3 and from nonuser is $7. The difference in cost results because nonusers are difficult to locate. a) Existing records give N₁ = 107, N₂ = 50, №3 = 152 and N4 = 68. Find the approximate sample size and allocation necessary to estimate the population proportion with a bound of 5% on the error of estimation. b) Suppose for the sample data captured after this survey was conducted yielded the following proportion of families who will use the new facilities: ₁ = .86,₂ = .94,3 = .65 and 4 = .55 Estimate the population proportion p, and place a bound on the error of estimation. Was the desired bound achieved? * c) Suppose that the total cost of sampling is fixed at $600. Choose the sample size and allocation that minimiz.es the variance of the estimator pst for this fixed cost.
Transcribed Image Text:to Just 6) A county government is interested in expanding the facilities of a day-care center for mentally disabled children. The expansion will increase the cost of enrolling a child in the center. A sample survey will be conducted to estimate the proportion of families with disabled children that will make use of the expanded facilities. The families are divided into those who use the existing facilities and those who do not. Some families live in the city in which the center is located, and some live in the surrounding suburban and rural areas. Thus, stratified random sampling is used, with users in the city, users in the surrounding country, nonusers in the city, and nonusers in the country forming strata 1, 2, 3, and 4, respectively. Approximately 90% of the present users and 50% of the present nonusers will use the expanded facilities. The cost of obtaining an observation from a user is $3 and from nonuser is $7. The difference in cost results because nonusers are difficult to locate. a) Existing records give N₁ = 107, N₂ = 50, №3 = 152 and N4 = 68. Find the approximate sample size and allocation necessary to estimate the population proportion with a bound of 5% on the error of estimation. b) Suppose for the sample data captured after this survey was conducted yielded the following proportion of families who will use the new facilities: ₁ = .86,₂ = .94,3 = .65 and 4 = .55 Estimate the population proportion p, and place a bound on the error of estimation. Was the desired bound achieved? * c) Suppose that the total cost of sampling is fixed at $600. Choose the sample size and allocation that minimiz.es the variance of the estimator pst for this fixed cost.
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