Question

Determine the point estimate of the population proportion and the margin of error for the following confidence interval.Lower boundequals0.212​,upper boundequals0.758​,nequals1200The point estimate of the population proportion is . 485.​(Round to the nearest thousandth as​ needed.)The margin of error is 0.273.​(Round to the nearest thousandth as​ needed.)

Answer 1

Answer: The point estimate of the population proportion is . 485.​

The margin of error is 0.273.​

Explanation:

Confidence interval for population proportion(p):

sample proportion ± Margin of error

Given: Lower bound of confidence interval = 0.212

Upper bound = 0.758

⇒sample proportion - Margin of error=0.212 (i)

sample proportion + Margin of error= 0.758 (ii)

Adding (i) and (ii) , we get

2(sample proportion) =0.970

⇒ sample proportion = 0.970÷2= 0.485

Since sample proportion is the point estimate of the population proportion.

So, the point estimate of the population proportion= 0.485

Now put sample proportion =0.485 in (ii), we get

0.485+ Margin of error= 0.758

⇒ Margin of error= 0.758 - 0.485 =0.273

i.e. The margin of error is 0.273.​