In: Statistics and Probability
A survey of 1100U.S. adults found that 31%of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the
90%confidence interval of the true proportion. Round intermediate answers to at least five decimal places. Round your final answers to at least three decimal places.
Solution =
Given,
n = 1100 ....... Sample size
Let
denotes the sample proportion.
Our aim is to construct 90% confidence interval.
/2
= 0.10
2 = 0.05 and 1-
/2 = 0.950
Now , the margin of error is given by
= 1.645 *
[ 0.31 *(1 - 0.31 ) / 1100 ]
= 0.02294
Now the confidence interval is given by
( 0.31 - 0.02294 )
( 0.31 + 0.02294 )
Required 90% Confidence Interval is ( 0.287 , 0.333 )