Question

In a survey of 1,532 former UF students, 84% said they were still in love with Tim Tebow. The survey's sampling error was 2%. Using this information, construct a confidence interval for the proportion of all former UF students who are still in love with Tim Tebow.

Answer 1

confidence interval for the proportion of all former UF students who are still in love with Tim Tebow.

(0.79 , 0.89)

Explanation:

step 1:-

Given sample survey former UF students n = 1532

84% said they were still in love with Tim Tebow

p = 0.84

The survey sampling error

`= \sqrt{(p(1-p))/(n) }`

Given standard error of proportion = 2% =0.02

Step 2:-

The 99% of z- interval is 2.57

The 99% of confidence intervals are

p ± zₐ S.E (since sampling error of proportion =
`\sqrt{(pq)/(n) }`

`(0.84 - 2.57X0.02 , 0.84 + 2.57X0.02)`

on simplification , we get

(0.84 - 0.0514 , 0.84 + 0.0514)

(0.79 , 0.89)

conclusion:-

confidence interval for the proportion of all former UF students who are still in love with Tim Tebow.

(0.79 , 0.89)