1,200 employees of a company were surveyed to find out whether they were satisfied with the company’s insurance policy. the survey showed that 80% of the respondents were not satisfied with the policy.
the standard error of the proportion is %. the number of people who are satisfied with the policy is between % and %.
nextreset

S.E = 0.01154 = 1.154 %

( 18.85% < p% < 21.15% )    

Step-by-step explanation:

Given:

- The proportion satisfied with the policy p = 0.2

- The proportion satisfied with the policy q = 0.8

- Size of sample n = 1,200

Find:

The standard error of the proportion

The interval of proportion of people satisfied with the policies.

Solution:

- The standard error of proportion of a sample s given by:

                                S.E = sqrt ( p*q / n )

Plug in the values:

                                S.E = sqrt ( 0.8*0.2 / 1200 )

                                S.E = 0.01154 = 1.154 %

- The interval of proportion of people satisfied is given by:

                                 ( p - S.E < p < p + S.E )

Plug values in:

                                 ( 0.2 - 0.01154 < p < 0.01154 + 0.2 )  

                                 ( 0.18846 < p < 0.21154 )  

                                 ( 18.85 < p% < 21.15 )