Question

A random sample of 500 apples was taken from large consignment and 45 of them were found to be bad. Find the limits at which the bad apples lie at 99% confidence level.

Answer 1

Sample size n = 500 

Proportion of bad apples P = 45/500 = 0.09 

So proportion of good apples Q = 1 – 0.09 = 0.91

The confidence limits for population proportion are given by,

= (0.09 – (2.58) (0.013), 0.09 + (2.58) (0.013)) . 

= (0.09 – 0.034, 0.09 + 0.034) 

= (0.056, 0.124) 

Thus the bad apples lie between 5.6% and 12.4%