Question

The mayor of a small city has suggested that the state's Corrections Department construct a new prison in his city, as he believes the project will result in better employment options for the adult citizens in his city. To estimate public support for such a project, corrections officials host a forum and discover that 31 of 183 adult citizens in attendance are in favor of the project. Assume that the citizens who attend the forum are representative of the city's adult citizens.

• If p̂p^ is the sample proportion of adult citizens attending the forum who are in favor of the project, calculate the value of this statistic and the standard error of this statistic.
• Construct and interpret a 98 percent confidence interval to estimate the population proportion of the city's adult citizens who are in favor of the project.

Answer 1

x = 31

n = 183

= x/n = 31/ 183= 0.169

= 0.169

SE = 0.028

98% CI

z value for 98% CI = 2.326

Margin of error = 2.326 * 0.028 = 0.064

CI = + /- E = ( 0.105 , 0.234)

CI = ( 0.105 ,   0.234)

We are 98% confident that the proportion of adult citizens attending the forum who are in favor of the project lies within

CI = ( 0.105 , 0.234)