Question

A poll asked the question, "What do you think is the most important problem facing this country today?" Twenty-four 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	%

A research group conducted an extensive survey of 3087 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, "What does success mean to you?" 1646 responded, "Personal satisfaction from doing a good job." Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. Find a 90% confidence interval for p. (Round your answers to three decimal places.)

lower limit
upper limit

Answer 1

1)

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.24 - 0.04 < p < 0.24 + 0.04

0.20 < p < 0.24

Lower limit = 20%

Upper limit = 24%

(2)

Lower limit = 0.518

Upper limit = 0.548