Question

A polling organization surveyed 2,000 residents of a town for their views on the mayor, and 1,640 respondents said they approved of the mayor. The organization then published a report of its findings, stating a range of the percentages of residents who approve of the mayor with 95% confidence. Based on this information, what is the lowest possible percentage of residents who approve of the mayor?

Answer 1

See image below

Explanation:

Answer 2

80.32%

Explanation:

The proportion who approved of the mayor :

p = number who approved of the mayor / total respondents = 1640 / 2000 = 0.82

The confidence interval for proportion is given by :

p ± Zcritical * √p(1 - p) / n

Zcritical at 95% = 1.96 (Z standard table distribution)

0.82 ± 1.96 * √0.82(0.18) / 2000

0.82 ± 1.96 * 0.0085906

0.82 ± 0.0168377

(0.8032 ; 0.8368)

Lower boundary = 0.8032