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.)


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
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