Question

In a survey of 1500 U.S. workers who are working from home, 885 of them would prefer to keep doing so after restrictions are lifted. Construct a 99% confidence interval for the population proportion of U.S workers who would like to keep working from home.

Answer 1

Solution :

Given that,

n = 1500

x = 885

Point estimate = sample proportion = = x / n = 885/1500=0.59

1 -   = 1-0.59 =0.41

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* (((0.59*0.41) / 1500)

= 0.0327

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.59-0.0327 < p <0.59+ 0.0327

0.5573< p < 0.6227

The 99% confidence interval for the population proportion p is : 0.5573,0.6227