Question

Determine the standard error of proportion for a random sample of 500 pineapples was taken from a large consignment and 65 were found to be bad

Answer 1

Sample size n = 500

No. of bad pine apples = 65

Sample proportion = P = ${\displaystyle \frac{65}{100}}$ = 0.13

Q = 1 – p

⇒ Q = 1 – 0.13

∴ Q = 0.87

The S.E for sample proportion is given by

S.E = ${\displaystyle \sqrt{\frac{\text{PQ}}{\text{N}}}}$

= ${\displaystyle \sqrt{\frac{\left(0.13\right)\left(0.87\right)}{500}}}$

= ${\displaystyle \sqrt{\frac{0.1131}{500}}}$

= ${\displaystyle \sqrt{0.0002262}}$

= 0.01504

∴ S.E = 0.015

Hence the standard error for sample proportion is S.E = 0.015