Question

A simple random sample of size n=450 individuals who are currently employed is asked if they work at home at least once per week. Of the 450 employed individuals​ surveyed, 33 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. The lower bound is ____.

Answer 1

GIVEN:

Sample size

(n) = 450

Number of employees who responded that they did work at home at least once per week

( х33 )

FORMULA USED:

The 99% confidence interval for population proportion is,

$p_{hat}\pm z_{c}*[[p_{hat}(1-p_{hat})]/n]^{1/2}$

where
Phat
is the sample proportion and is the sample size.

CALCULATION:

The sample proportion is,

(Phat)

$p_{hat}=x/n$

  

33/450

  

-0,073

The z critical value at 99% confidence level is .

2.58

The 99% confidence interval for population proportion of employed individuals who work at home at least once per week is given by,

$p_{hat}\pm z_{c}*[[p_{hat}(1-p_{hat})]/n]^{1/2}$

   $=0.073 \pm 2.58*[[0.073(1-0.073)]/450]^{1/2}$

0.0414,0.1046

The 99% confidence interval for population proportion of employed individuals who work at home at least once per week is .

0.0414,0.1046

The lower bound is and the upper bound is .

Thus there is a 99% chance that the confidence interval
0.0414,0.1046
contains the true population proportion of employed individuals who work at home at least once per week.