Question

In a survey of 3203 ​adults, 1462 say they have started paying bills online in the last year. Construct a​ 99% confidence interval for the population proportion. Interpret the results. A​ 99% confidence interval for the population proportion is left parenthesis nothing comma nothing right parenthesis . ​(Round to three decimal places as​ needed.)

Answer 1

Solution:

Confidence Interval for population proportion(p)

Given,

n = 3203   ....... Sample size

x = 1462   .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n = 1462/3203 = 0.4564

Our aim is to construct 99% confidence interval.

c = 0.99

= 1- c = 1- 0.99 = 0.01

  /2 = 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 is the critical value.

Now , confidence interval for population proportion(p) is given by:

     

0.4564 - 2.576 *    

0.4564 + 2.576 *

0.434 <     < 0.479

the required 99% confidence interval for the population proportion is (0.434 , 0.479)