Question

A poll asked the question, "What do you think is the most important problem facing this country today?" Twenty percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 2 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 2970 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?" 1482 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

Solution :

1) Given that,

Point estimate = sample proportion = = 0.20

Margin of error = E = 0.02

A 95% confidence interval for population proportion p is ,

± E

= 0.20  ± 0.02

= ( 0.18, 0.22 )

lower limit = 18%

upper limit = 22%

2) Given that,

n = 2970

x = 1482

Point estimate = sample proportion = = x / n = 1482 / 2970 = 0.499

1 - = 1 - 0.499 = 0.501

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05  = 1.645

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

= 1.645 (((0.499 * 0.501) / 2970)

= 0.015

A 90% confidence interval for population proportion p is ,

± E   

= 0.499  ± 0.015

= ( 0.484, 0.514 )

lower limit = 0.484

upper limit = 0.514