A sample survey of households in a community containing 1500 households is to be conducted for...
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A sample survey of households in a community containing 1500 households is to be conducted for the purpose of determining the total number of persons over 18 years of age in the community who have one or more permanent teeth (other than third molars) missing. Since this variable is thought to be correlated with age and income, the strata shown in the accompanying table are formed by using available population data. A stratified random sample of 100 families is to be taken. Stratum Variable Age Mean Standard deviation Annual family income (x$1000) Mean Standard deviation No. of families 1 2 4 30 32 25 27 15 15 10 10 8 2 300 500 100 600 15 7 15 3 a. Determine the number of families to be taken from each stratum if proportional allocation is used. b. Determine the number of families to be taken from each stratum if optimal allocation is used based on annual family income. c. Determine the number of families to be taken from each stratum if optimal allocation is used based on age. d. How would you allocate sample to strata, taking into consideration both age and annual family? e. Suppose the number of persons over 18 years of age having missing teeth in a family is highly correlated with family income. Is stratified random sampling with proportional allocation likely to yield an estimate having lower variance than that obtained from a simple random sample of the same number of households? A sample survey of households in a community containing 1500 households is to be conducted for the purpose of determining the total number of persons over 18 years of age in the community who have one or more permanent teeth (other than third molars) missing. Since this variable is thought to be correlated with age and income, the strata shown in the accompanying table are formed by using available population data. A stratified random sample of 100 families is to be taken. Stratum Variable Age Mean Standard deviation Annual family income (x$1000) Mean Standard deviation No. of families 1 2 4 30 32 25 27 15 15 10 10 8 2 300 500 100 600 15 7 15 3 a. Determine the number of families to be taken from each stratum if proportional allocation is used. b. Determine the number of families to be taken from each stratum if optimal allocation is used based on annual family income. c. Determine the number of families to be taken from each stratum if optimal allocation is used based on age. d. How would you allocate sample to strata, taking into consideration both age and annual family? e. Suppose the number of persons over 18 years of age having missing teeth in a family is highly correlated with family income. Is stratified random sampling with proportional allocation likely to yield an estimate having lower variance than that obtained from a simple random sample of the same number of households?
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Related Book For
Business Statistics a decision making approach
ISBN: 978-0133021844
9th edition
Authors: David F. Groebner, Patrick W. Shannon, Phillip C. Fry
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