Question

Answers
Point Estimate
Standard Error
Margin of Error
Alpha
Critical Value
Confidence Interval

During a national debate on changes to health care, a cable news service performs an opinion poll of 500 small business owners.  It shows that 325 of small-business owners do not approve of health care changes.  Develop a 95% confidence interval for the proportion opposing health care changes.   

  

Answer 1

Solution :

Given,

n = 500 ....... Sample size

x = 325 .......no. of successes in the sample

Let denotes the sample proportion.

     = x/n   = 325/500 = 0.65  

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 * [ 0.65 *(1 - 0.65)/500]

E = 0.042

Now the confidence interval is given by

( - E)   ( + E)

( 0.65 - 0.042)   ( 0.65 + 0.042 )

   0.608   0.692  

Required 95% Confidence Interval is ( 0.608 , 0.692 )