Homework Help

n=200, x=40, 95%confidence  Use the sample data and confidence level to construct the...

user profile pic

surfer3 | Valedictorian

Posted May 30, 2012 at 7:01 PM via web

dislike 2 like

n=200, x=40, 95%confidence

 

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p.

1 Answer | Add Yours

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 30, 2012 at 9:17 PM (Answer #1)

dislike 1 like

A confidence of 95% implies that `alpha=.05,alpha/2=.025`

`hatp=40/200=.2`

`n=200`

`z_(alpha/2)=1.96` from a table.

The interval we seek is given by:

`hatp-z_(alpha/2)sqrt((hatp(1-hatp))/n)<p<hatp+z_(alpha/2)sqrt((hatp(1-hatp))/n)`

Thus:

`.2-1.96sqrt((.2(.8))/200)<p<.2+1.96sqrt((.2(.8))/200)`  or approximately:

.1446<p<.2554

Thus, with 95% confidence, we can say that 14.5%<p<25.5%

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes