In: Math
A farmer randomly samples 600 eggs and finds that 28 are bad. Find a 95% confidence interval for the actual proportion of bad eggs.
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 = Z0.025 = 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)