Question

There are 2,000 eligible voters in a precinct. A total of 400 voters are randomly selected and asked whether they plan to vote for the Democratic incumbent or the Republican challenger. Of the 400 surveyed, 295 said they would vote for the Democratic incumbent. Using the 0.90 confidence level, construct a confidence interval for the proportion that plan to vote for the Democratic incumbent?

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 295 / 400 = 0.738

1 - = 1 - 0.738 = 0.262

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.738 * 0.262) / )

= 0.036

A 90% confidence interval for population proportion p is ,

± E   

= 0.738  ± 0.036

= ( 0.702, 0.774 )