Question

We wish to estimate what percent of adult residents in a certain county are parents. Out of 300 adult residents sampled, 102 had kids. Based on this, construct a 95% confidence interval for the proportion p of adult residents who are parents in this county.

Answer 1

Answer:

The answer is "$0.34 \pm 0.060$".

Step-by-step explanation:

Point estimate = Sample proportion $= \frac{102}{300}= 0.34$

For $95\%$ confidence, $z = 1.96$

Hence,

Margin of error$= 1.96 \times \sqrt{0.34\times \frac{0.84}{300}}=1.96 \times 0.0308 = 0.060$

Therefore,

Confidence interval in the tri-equality form:

$\to 0.34 - 0.060 < p < 0.34 + 0.060\\\\\to 0.28 < p < 0.4$

Confidence interval using point estimate and margin of error:

$p = 0.34 \pm 0.060$