Question

the homeownership rates in a certain country have been declining. the countrys homeownership rate was 48.6% in 2017 (compared to 65.2% another country). suppose, from a random sample of 269 households in the country in 2018, 115 were occupied by the owners of the residence parts a through c.
a. construct a 98% confidence interval to estimate the actual proportion of households in the country that are occupied by their owners in 2018.
the confidence interval has a lower limit of 0.357 and an upper limit of 0.498.
(round to three decimal places as needed.)
b. what is the margin of error for this sample?
the margin of error is
(round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for margin of error

The margin of error \(E\) for a confidence interval of proportion is given by \(E=\text{Upper limit}-\text{Sample proportion}\) or \(E = \text{Sample proportion}-\text{Lower limit}\). Also, \(E=\frac{\text{Upper limit}-\text{Lower limit}}{2}\)

Step2: Calculate the margin of error using the formula \(E=\frac{\text{Upper limit}-\text{Lower limit}}{2}\)

Given lower limit \(L = 0.357\) and upper limit \(U=0.498\)

$$
LATEXBLOCK0
$$

Answer:

\(0.071\)