Question

In a survey of 2004 American adults, 501 of them said that they believed in astrology

(a) Calculate and interpret a confidence interval at the 95% confidence level for the proportion of all adult American adults who believe in astrology.

(b) Calculate and interpret a 95% lower confidence bound for the proportion of all adult American adults who believe in astrology.

Please be very detailed by showing every step

Answer 1

Answer:

n= 2004, x= 501, C= 95%

a) formula for 2 sided confidence interval is

Where Zc is the z critical value for C= 95%

Zc= 1.96

0.23104 < P < 0.26896

thus we get confidence interval as ( 0.23104 , 0.26896 )

Therefore we are 95% confident that the proportion of all adult American

adults who believe in astrology is between 0.23104 to 0.26896

b)

formula for lower sided confidence bound is

Where Zc is the z critical value for C= 95%

Zc= 1.96

0.23104  

thus we get lower confidence bound as = 0.23104

Therefore we are 95% confident that the proportion of all adult American

adults who believe in astrology is greater then 0.23104