Construct the 95% confidence interval estimate to the population. Of the 1,220 inmates interviewed, 178 said they committed another offense within 1 year of release from jail.

Answer 1

z value at 95% = 1.96

The sample proportion for population:

proportion = 178/1220 = .1459

p(1-p) / n= .1459 (1-.1459) / 1220 = .000102141959

square root of .000102141959 = .0101065

Margin of Error

= 1.96 * .0101065 . = .019808799 = 1.981

178/1220 = 14.59% +- 1.98%

12.61- 16.57

With 95% confidence the number of inmates that will commit a crime within one year is somewhere between 12.61 and 16.57 based on this sample.