Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Of 125 adults selected randomly from one town, 31 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.n

Answer 1

Solution :

Given,

n = 125 ....... Sample size

x = 31 .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n   = 31 /125 = 0.248  

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 * [.0.248 *(1 - 0.248)/125]

= 0.099

Now the confidence interval is given by

( - E)   ( + E)

( 0.248 - 0.099 )   ( 0.248 + 0.099 )

0.149   0.347  

Required 99% Confidence Interval is ( 0.149 , 0.347 )