Question

A statewide poll was conducted between the governor race in Georgia between Democratic Stacey Abrams and Republican Brian Kemp. In the poll, Abrams had 46.9 percent of likely voters, and Kemp had 47.7 percent of likely voted. The results covered 1091 registered voters.

Report the 95 percent confidence intervals for Abrams and Kemp. Do they overlap or not?

Answer 1

Let p₁ and p₂ denote the per cent/proportion of voters likely to support Abrams and Kemp respectively. Given n = 1091.

The 100(1-)% CI for the proportion can be constructed using the formula:

Given:

Here, = 0.05, hence, Z can be obtained from standard normal table, by looking for the area 1 - 0.05/2 = 0.975:

We get Z = 1.96

1. The 95% CI for the proportion of voters supporting Abram:

= (0.439,0.499).....................(1)

2.The 95% CI for the proportion of voters supporting Kemp:

= (0.447,507).........................(2)

From (1) and (2), we find that both intervals encloses the values ranging from 0.447 to 0.499. Hence, we may conclude that the two intervals do overlap.