In: Statistics and Probability
In a recent presidential election, 611 voters were surveyed and 308 of them said that they voted for the candidate who won. a) Find the point estimate of the percentage of voters who said that they voted for the candidate who won. b) Find a 98% confidence interval estimate of the percentage of voters who said that they voted for the candidate who won.
Solution :
Given that,
n = 611
x = 308
(a)
Point estimate = = x / n = 308 / 611 = 0.504
1 - = 1 - 0.504 = 0.496
At 98% confidence level the z is ,
= 1 - 98% = 1 - 0.98 = 0.02
/ 2 = 0.02 / 2 = 0.01
Z/2 = Z0.01 = 2.326
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.326 * (((0.504 * 0.496) / 611)
= 0.047
(b)
A 98% confidence interval for population proportion p is ,
- E < P < + E
0.504 - 0.047 < p < 0.504 + 0.047
0.457 < p < 0.551
(0.457 , 0.551)