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

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

Explanation:

Point estimate = Sample proportion
`= (102)/(300)= 0.34`

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

Hence,

Margin of error
`= 1.96 * \sqrt{0.34* (0.84)/(300)}=1.96 * 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`