Question

3. In a survey to estimate average household monthly medical expenses, 500 households were selected at random from a population of 5000 households. Of the selected households, 336 had children in the household and 164 had no children. A stratified subsample of 112 households with children and 41 households without children was then selected, and monthly medical expendi- ture data were collected from households in the subsample. For the households with deviation of 160; for the households without children, the respective figures were $110 and 60. Estimate mean monthly medical expenditure for households in the population, and estimate the variance of the estimate. children, the sample mean expenditure was $280 with a sample standard

Answer 1

We have two stratas here, 'households with children' and 'households without children'. To calculate the mean monthly medical expenditure for households:

Here, N_h is the number of units in strata which are 336 and 164.

x is the sample mean

N = 336 + 164 = 500

Hence, Mean = 1/500 * (336*280 + 164*110)

Mean = 224.24

Variance can be found by:

Nh Tth h-1

n_h is the number of observations in each strata which is 112 and 41.

Variance:  

3362 336 112, 160 160 /1642 164- 41,60x 60 121 336 500 164

Variance = 68.8 + 7.0848 = 75.8848

Hence, the mean of the sample is 224.24 and variance is 75.8848.