Question

In a survey of 938 U.S. adults, 235 say the phrase "you know" is the most annoying conversational phrase. Let p be the proportion of the population who respond yes. Use the given information to Construct a 90% confidence interval for p.

Answer 1

CI 90% = ( 0.227 ; 0.273)

Explanation:

Information from the survey:

sample size n = 938

number of people with yes answer x = 235

proportion of people p = 235/938

p = 0.25 then q = 1 - 0.25 q = 0.75

Confidence Interval 90 % .

CI 90% = ( p ± SE )

CI 90% = ( p ± z(c)*√(p*q)/n)

CI 90 % then significance level is α = 10 % α/2 = 5%

α/2 = 0.05 we find in z-table z (c) = 1.64

√(p*q)/n = √0.25*0.75/938

√(p*q)/n = √0.000199

√(p*q)/n = 0.014

CI 90% = ( p ± z(c)*√(p*q)/n)

CI 90% = ( 0.25 ± 1.64*0.014)

CI 90% = ( 0.25 ± 0.023 )

CI 90% = ( 0.227 ; 0.273)