Question

Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 153 supported her. Construct a 90% confidence interval on the population proportion for the support of candidate A in the following election.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 153 / 300 = 0.510

1 - = 1 - 0.510 = 0.49

Z/2 = 1.645

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

= 1.645 * (((0.510 * 0.49) / 300)

Margin of error = E = 0.047

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.510 - 0.047 < p < 0.510 + 0.047

0.463 < p < 0.557

The 90% confidence interval for the population proportion p is : 0.463 , 0.557