Question

6 of 6 (2 complete) am 6.3.14-T In a survey of 2259 adults, 741 say they believe in UFOs. Construct a 95% confidence interval for the population proportion of adults who believe in UFOs. A 95% confidence interval for the population proportion is (D). (Round to three decimal places as needed.)

Answer 1

n = number of adults in a survey = 2259

x = number of adults who believe in UFOs = 741

Sample proportion:

$\hat{p}=\frac{x}{n}=\frac{741}{2259}=0.3280$ (Round to 4 decimal)

Confidence level = c = 0.95

A 95% Confidence interval for the population proportion is

p*(1-7) p*(1-P) P - %* <p < +%* V n n

where zc is z critical value for (1+c)/2 = (1+0.95)/2 = 0.975

zc = 1.96 (From statistical table of z values)

$0.3280-1.96*\sqrt{\frac{0.3280*(1-0.3280)}{2259}}<p<0.3280+1.96*\sqrt{\frac{0.3280*(1-0.3280)}{2259}}$

$0.3280-1.96*\sqrt{\frac{0.220416}{2259}}<p<0.3280+1.96*\sqrt{\frac{0.220416}{2259}}$

(Round to 3 decimal)

A 95% Confidence interval for the population proportion is (0.309, 0.347)