Question

A sample of 692 families was selected from a large region to determine, among other things, the proportion of families with vegetable gardens. The families were classified into three strata - urban, rural non farm and farm - because these groups were expected to show differences in the frequency and size of vegetable gardens. The sampling fraction was roughly the same in all strata, a sample of 1 per 1000 being aimed at. The values of the population weights (Wi), the stratum sample sizes (ni) and the number of families with vegetable gardens (xi) are shown in the table.

Stratum (i) W 0.445 300 218 Urban 155 0.230 147 Rural non-farm 0.325 237 229 Farm Total 692 594

a) estimate the population proportion of families with vegetable gardens and given an approx 95% confidence interval for it.

b) ignoring the stratification, use simple random sampling to estimate the population proportion of families with vegetable gardens and given an approx 95% confidence interval for it. Comment briefly on the precision of the estimates in part (a) and part (b).

Question on stratified sampling finding proportions and CI's for stratified sampling and SRS, please help! Will thumbs up. Thanks

Answer 1

Page No. Date Solution The populatio proportionn of familieg coith vegetable gadens det is1 ohere p: gample p TOPOrtion of itotratum -1,2,9 , compute fi ese get 1, 2, 3 this for egch j Pi 218 300 O-948 3 147 185 & 69 692 &584 fg 229 C 0.9 662 237 equation EWi Pi T-1 becomes s 0448x0.72664 0.290X0.9483 + 0.826X0. 9662 08554 interval 96.10 CO0tidence is given Wi pigi (Pat) Var

Page No j Datel Nas (P Pi9i ali 02=155 Nar 00013 .0000 16 +0-000014 1 O 00016 46.1 COnfid en ce foteryalis var(Pat Oro1264 .8954 41-g6 (0.0126 O8554-1.96x0001 8806 O.8801 6y using Simple Random Sampling - 594 600 O99 N-O VaT 13 No-P 0 000004412 O.0021 Vas 9S Confidence interval for 9RS is

Date O-99 +le96x0.00 21 L0.99 0-99 t19e xO.0021 1-96 X0.002 O9858 0.9941 Here length in SRO metbd Hemce in the given prmblem simple Randlom ap ling of confidence interval is very ghort ts more prectse estimate.