Question

If n = 460 and X = 368, construct a 99% confidence interval for the population proportion, p.

Give your answers to three decimals

Answer 1

Solution :

Given that,

n = 460

x = 368

Point estimate = sample proportion = = x / n = 368/460=0.8

1 -   = 1-0.8 =0.2

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.8*0.2) /460 )

E = 0.048

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.8-0.048 < p <0.8+ 0.048

0.752< p < 0.848

The 99% confidence interval for the population proportion p is : 0.752, 0.848