Question

A market research company conducted a survey to find the level of affluence in a city. They defined the category "affluence" for people earning $100,000 or more annually. Out of 267 persons who replied to their survey, 32 are considered affluent. What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place. 0.08 to 0.34 0.08 to 0.16 0.24 to 0.34 0.16 to 0.24

Answer 1

0.08 ; 0.16

Explanation:

Given :

x = 32 ; n = 267 ; phat = x / n = 32 / 267 = 0.11985

The Zcritical at 95% = 1.96

The confidence interval for proportion :

C. I = Phat ± Z*√(phat(1-phat))/n

C. I = 0.11985 ± 1.96√(0.11985(1-0.11985))/267

C. I = 0.11985 ± 1.96(0.0198765)

C. I = 0.11985 ± 0.0389581

C. I = 0.08 ; 0.158

C. I = 0.08 ; 0.16