Constructing confidence intervals

Question

An interactive poll found that 362 of 2,243 adults aged 18 or older have at least one tattoo.
(a) Obtain a point estimate for the proportion of adults who have at least one tattoo.
(b) Construct a 90% confidence interval for the proportion of adults with at least one tattoo.
(c) Construct a

99% confidence interval for the proportion of adults with at least one tattoo.
(d) What is the effect of increasing the level of confidence on the width of the interval?

Answer 1

The article at the following link is helpful:

 

http://www.dummies.com/education/math/statistics/how-to-determine-the-confidence-interval-for-a-population-proportion/

 

(a) the sample proportion serves as  your initial point estimate:  p-hat = 362/2243=.161391 or just over 16%

 

(b)  Plugging z = 1.9645 ,  n=2243, and p-hat = .161391 into the formula shown in the article,

                your margin of error is .01526 or just over 1.5%

       With 90% certainty, the actual population proportion lies in the interval ( .161391 - .01526 , .161391 + .01526) =

                                                                                                                     ( .146161,  .176651)

 

(c) Repeating the same process, this time z=2.58, per MS Excel, the confidence interval is (0.141349759 0.181432229)

     with error margin 0.020041235 or just over 2%

 

(d) As expected, the typical trade-off is between higher confidence and degree of certainty in exchange for

      larger margin of error which widens the window width of the confidence interval