Question

In a survey regarding an upcoming presidential primary, 1000 people were asked whether or not they favor a particular candidate. 214 of the respondents indicated that they favor the candidate. Form a 95% confidence interval for the proportion of voters who favor the candidate.

Answer 1

Solution :

Given that,

n = 1000

x = 214

Point estimate = sample proportion = = x / n = 214/1000=0.214

1 - = 1-0.214=0.786

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96} ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )   

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

= 1.96 (((0.214*0.786) /1000 )

= 0.013

A 95% confidence interval for the proportion of voters who favor the candidate.

- E < p < + E

0.214-0.013 < p < 0.214+0.013

0.201< p < 0.227

95% confidence interval for the proportion of voters who favor the candidate.

(0.201,0.227)