Question

If n = 320 and ˆ p (p-hat) = 0.15, construct a 99% confidence interval.

Give your answer to three decimals __<P<___

Answer 1

Solution:

Given ,

n = 320

= 0.15

c = 99% = 0.99

Our aim is to construct 99% confidence interval.

c = 0.99

= 1- c = 1- 0.99 = 0.01

  /2 = 0.005 and 1- /2 = 0.995

Search the probability 0.995 in the Z table and see corresponding z value

= 2.576   

Now , the margin of error is given by

E = /2 *  

= 2.576* [0.15 *(1 - 0.15)/320]

= 0.051

Now the confidence interval is given by

( - E)   ( + E)

(0.15 - 0.051)   (0.15 + 0.051)

0.099    0.201