Question

 A wholesaler in apples claims that only 4% of the apples supplied by him are defective. A random sample of 600 apples contained 36 defective apples. Calculate the standard error concerning of good apples

Answer 1

Sample size = 600

Number of success = 600 – 36

= 564

Sample proportion p = `564/600` = 0.94

= 600

Population proportion (p) = probability of getting good apple

= 96%

= `96/100` .......{∵ 4% of the apples 100 are defective}

P = 0.96

Q = 1 – p = 1 – 0.96

Q = 0.04

The S.E for a sample proporation is given by

S.E = `sqrt("PQ"/"N")`

= `sqrt(((0.96)(0.04))/600`

= `sqrt(0.0384/600`

= `sqrt(0.000064)`

∴ S.E = 0.008

Hence the standard error for sample proportion is S.E = 0.008