Question

A random sample of 5697 physicians in Colorado showed that 2927 provided at least some charity care.

(b) Find a 99% confidence interval for p.

lower limit-

upper limit-

Answer 1

Solution :

Given that,

n = 5697

x = 2927

Point estimate = sample proportion = = x / n = 2927/ 5697 = 0.514

1 - = 1-0.514 = 0.486

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z_{0.005 = 2.576}

Z/2 = 2.576

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

= 2.576* ((0.514*(0.486) /5697 )

= 0.017

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.514 -0.017< p < 0.514 +0.017

0.497< p < 0.531

( 0.497,0.531 )

lower limit- 0.497

upper limit-0.531