Question

A farmer randomly samples 600 eggs and finds that 28 are bad. Find a 95% confidence interval for the actual proportion of bad eggs.

Answer 1

Solution :

Given that,

n = 600

x = 28

Point estimate = sample proportion = = x / n = 28 / 600 = 0.047

1 - = 1 - 0.047 = 0.953

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.047*0.953) /600 )

= 0.017

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.047 - 0.017< p <0.047 + 0.017

0.030< p <0.064

The 95% confidence interval for the population proportion p is : (0.030 , 0.064)