Question

A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of n employees produced the following 98% confidence interval for the proportion of employees who prefer plan A: (0.241, 0.561). Identify the point estimate for estimating the true proportion of employees who prefer that plan

Answer 1

Answer:

the point estimate of the true proportion of employees is 0.401

Step-by-step explanation:

Given data

plan A = ( 0.241 , 0.561 )

to find out

the point estimate for estimating the true proportion of employees who prefer that plan

solution

we know that given data 98% confidence interval for the proportion of employees who prefer plan A: (0.241, 0.561) so point estimate for estimating the true proportion o employees who prefer that plan is p^E

and we can say here  

lower limit = $p^{-E}$ = 0.241    ..............1

upper limit = $p^{+E}$  = 0.561    ...............2

now add these two equations 1 and 2

=  $p^{-E}$ + $p^{+E}$

=  $p^{-E}$ + $p^{+E}$  = 0.241 + 0.561

2 p = 0.802

2p = 0.806

p = 0.401

So the point estimate of the true proportion of employees is 0.401