Question

A sociologist is studying the prevalence of crime in one major city. In a sample of 150 randomly selected residents, 45 say that they have been victimized by a criminal. Based on this sample, construct a 95% confidence interval for the proportion of all residents in this city who have been victimized by a criminal. Then complete the table below.Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.)

What is the lower limit of the 95% confidence interval?
What is the upper limit of the 95% confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 45 / 150 = 0.30

1 - = 1 - 0.30 = 0.70

Z/2 = Z0.025 = 1.96

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

= 1.96 (((0.30 * 0.70) / 150 )

= 0.073

A 95% confidence interval for population proportion p is ,

± E   

= 0.30 ± 0.073

= ( 0.23, 0.37 )

lower limit = 0.23

upper limit = 0.37