In: Statistics and Probability
Given n =1000, x = 841, Find a 95% confidence interval for the proportion 841/1000 =.841
Solution :
Given that,
n = 1000
x = 841
Point estimate = sample proportion = = x / n = 841/1000=0.841
1 - = 1-0.841 =0.159
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 ( Using z table )
Margin of error = E = Z/2 * ((( * (1 - )) / n)
= 1.96 (((0.841*0.159) /1000 )
E = 0.023
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.841-0.023 < p <0.841+0.023
0.818< p < 0.864
(0.818 , 0.864)