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प्रश्न
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?
उत्तर
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
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