Question

Construct a 99​% confidence interval to estimate the population proportion with a sample proportion equal to 0.50 and a sample size equal to 200. LOADING... Click the icon to view a portion of the Cumulative Probabilities for the Standard Normal Distribution table. A 99​% confidence interval estimates that the population proportion is between a lower limit of nothing and an upper limit of nothing. ​(Round to three decimal places as​ needed.)

Answer 1

Solution :

Given that,

n = 200

   = 0.50

1 - = 1 - 0.50 = 0.50

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.50 * 0.50) / 200) = 0.091

A 99 % confidence interval for population proportion p is ,

- E < P < + E

0.50 - 0.091 < p < 0.50 + 0.091

0.409 < p < 0.591

The 99% confidence interval for the population proportion p is : ( lower limit = 0.409 upper limit =  0.591)