A regional government is interested in expanding the facilities of a day care center for mentally retarded children. day care center for mentally retarded children. The expansion will increase the cost of enrolling children in the center. A sample survey is to be conducted to estimate the proportion of families with affected children who will use the expanded facilities. The families are divided between those who use the current facilities and those who do not. Some families live in the city where the center is located, and others live in the surrounding suburban and rural areas. Thus, stratified random sampling is used with people from the city where the center is located. stratified sampling is used with people in the city using the facility, people in the surrounding area using the facility, people in the city not using the facility, and people in the surrounding area not using the facility, forming strata 1, 2, 3, and 4, respectively. Approximately 90% of current users and 50% of non-users will use the new facilities. The costs for observing a current user are $4.00 and $8.00 for a non-user. The difference in cost is due to the difficulty in locating non-users. The existing records give us N1 = 97, N2 = 43, N3 = 145 and N4 = 68. At Find the approximate sample size and the bias needed to estimate the population proportion with a limit of 0.05 for the estimation error. The survey is carried out and the following results are obtained proportion of households that will use the new facilities: pˆ1 = 0, 87 pˆ2 = 0, 93 pˆ3 = 0, 60 pˆ4 = 0, 53 Estimate the population p and establish a limit for the estimation error. Was the desired limit achieved? Assume that, in Exercise, the total cost of sampling is set at $400. Choose the sample size and the affixation that minimizes the variance of the estimator pˆst for this fixed cost. Translated with www.DeepL.com/Translator (free version)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.4: Collecting Data

Problem 6E

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A regional government is interested in expanding the facilities of a day care center for mentally retarded children. day care center for mentally retarded children. The expansion will increase the cost of enrolling children in the center. A sample survey is to be conducted to estimate the proportion of families with affected children who will use the expanded facilities. The families are divided between those who use the current facilities and those who do not. Some families live in the city where the center is located, and others live in the surrounding suburban and rural areas. Thus, stratified random sampling is used with people from the city where the center is located. stratified sampling is used with people in the city using the facility, people in the surrounding area using the facility, people in the city not using the facility, and people in the surrounding area not using the facility, forming strata 1, 2, 3, and 4, respectively. Approximately 90% of current users and 50% of non-users will use the new facilities. The costs for observing a current user are $4.00 and $8.00 for a non-user. The difference in cost is due to the difficulty in locating non-users. The existing records give us N1 = 97, N2 = 43, N3 = 145 and N4 = 68. At Find the approximate sample size and the bias needed to estimate the population proportion with a limit of 0.05 for the estimation error. The survey is carried out and the following results are obtained proportion of households that will use the new facilities: pˆ1 = 0, 87 pˆ2 = 0, 93 pˆ3 = 0, 60 pˆ4 = 0, 53 Estimate the population p and establish a limit for the estimation error. Was the desired limit achieved? Assume that, in Exercise, the total cost of sampling is set at $400. Choose the sample size and the affixation that minimizes the variance of the estimator pˆst for this fixed cost. Translated with www.DeepL.com/Translator (free version)

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