Question

In a sample of 500 registered voters, 314 of them said they support Bruce Wayne for the president of the US. Compute a 98% confidence interval for the true percent of support Bruce Wayne has.

Answer 1

Solution :

Given that,

n = 500

x = 314

Point estimate = sample proportion = = x / n = 314/500=0.628

1 -   = 1- 0.628 =0.372

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

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

= 2.326 (((0.628*0.372) / 500)

E = 0.05

A 98% confidence interval for proportion p is ,

- E < p < + E

0.628 - 0.05 < p < 0.628+0.05

0.578<p<0.678