Question

A poll asked the question, "What do you think is the most important problem facing this country today?" Nineteen percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 4 percentage points. Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters.

lower limit	%
upper limit	%

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 19% = 0.19

1 - = 1 - 0.19 = 0.81

Margin of error = E = 4% = 0.04

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.19 - 0.04 < p < 0.19 + 0.04

0.15 < p < 0.23

15% < p < 23%

Lower limit = 15%.

Upper limit = 23%