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 = ${\displaystyle \frac{3}{10.954}=\frac{230}{400}}$

p = 0.575

q = 1 – p

= 1 – 0.575

q = 0.425

Sample error S.E = ${\displaystyle \sqrt{\frac{\text{pq}}{\text{n}}}}$

= ${\displaystyle \sqrt{\frac{0.575\times 0.425}{400}}}$

= ${\displaystyle \sqrt{\frac{0.223125}{400}}}$

= ${\displaystyle \sqrt{0.0005578125}}$

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 = ${\displaystyle \frac{1}{2}}$ = 0.5

q = 1  – p

⇒ q = 1 – 0.5

q = 0.5

∴ Standard Error S.E = ${\displaystyle \sqrt{\frac{\text{pq}}{\text{n}}}}$

= ${\displaystyle \sqrt{\frac{0.5\times 0.5}{400}}}$

= ${\displaystyle \sqrt{\frac{0.25}{400}}}$

= ${\displaystyle \sqrt{0.000625}}$

= 0.025