Question

2.In a survey of 2344 ​adults, 721 say they believe in UFOs. Construct a 95 % confidence interval for the population proportion of adults who believe in UFOs. A 95​% confidence interval for the population proportion is (),()

Answer 1

Solution:

Given,

n = 2344 ....... Sample size

x = 721 .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n   = 721/2344= 0.3076

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.025 and 1- /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

= 1.96

Now , the margin of error is given by

E = /2 *  

= 1.96 * [0.3076 *(1 - 0.3076)/2344]

= 0.01868

Now the confidence interval is given by

( - E)   ( + E)

(0.3076 - 0.01868)   (0.3076 +0.01868 )

0.289    0.326

(0.289 , 0.326)