Question

A simple random sample of size n equals 400 individuals who are currently employed is asked if they work at home at least once per week. Of the 400 employed individuals​ surveyed 40 responded that they did work at home at least once per week. Construct a​ 99% confidence interval for the population proportion of employed individuals who work at home at least once per week.

Answer 1

ANSWER:

Given that:

A simple random sample of size n equals 400 individuals who are currently employed is asked if they work at home at least once per week.

Of the 400 employed individuals​ surveyed 40 responded that they did work at home at least once per week.

n=400

X=40

Point estimate = sample proportion

1 - = 1 - 0.1 = 0.9

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

= 0.012

A 99% confidence interval for population proportion p is ,

= 0.01- 0.02 < P < 0.02

= -0.002 <P< 0.022

The 99% confidence interval for the population proportion p is : ( -0.002 , 0.022 ).