Question

In a sample of 400 population from a village 230 are found to be eaters of vegetarian items and the rest non-vegetarian items. Compute the standard error assuming that both vegetarian and non-vegetarian foods are equally popular in that village?

Answer 1

Sample size n = 400

Case (i):

Sample proporation of vegetarian p = `3/10.954 = 230/400`

p = 0.575

q = 1 – p

= 1 – 0.575

q = 0.425

Sample error S.E = `sqrt("pq"/"n")`

= `sqrt((0.575 xx 0.425)/400)`

= `sqrt(0.223125/400)`

= `sqrt(0.0005578125)`

S.E = 0.2361

Case(ii):

Sample size n = 400

Since both vegetarian and non-vegetarian foods are equally popular in that village

Sample proparation of vegetarian p = `1/2` = 0.5

q = 1  – p

⇒ q = 1 – 0.5

q = 0.5

∴ Standard Error S.E = `sqrt("pq"/"n")`

= `sqrt((0.5 xx 0.5)/400)`

= `sqrt(0.25/400)`

= `sqrt(0.000625)`

= 0.025