A researcher examined a random sample of 300 homes in a small city and found that 47 had solar panels installed on their roofs.

Question

1 year ago

10

A researcher examined a random sample of 300 homes in a small city and found that 47 had solar panels installed on their roofs.

Use the sample to construct a 99% confidence interval for the proportion of all homes in the city that have solar panels installed on their roofs. What is the sample proportion? **Round to two decimal places

Mathematics

1 answer:

Rina8888 [55] · Answer 1 · 2023-03-02T17:13:34+03:00

The confidence interval for the sample proportion is $CI = 0.16 \pm 0.0545$

<h3>How to calculate the confidence interval for proportion?</h3>

The formula for calculating the confidence interval for proportion is expressed as:

$p \pm z\sqrt{p(1-p)/n$

p is the proportion

z is the z score at 99% interval

n is the sample size

Given the following parameters

$p=\frac{47}{300} = 0.16\\z=2.576\\n=300$

Substitute the values

$CI = 0.16 \pm 2.576\sqrt{0.16(0.84)/300}\\CI=0.16\pm2.576(0.02116)\\CI = 0.16 \pm 0.0545$

Hence the confidence interval for the sample proportion is $CI = 0.16 \pm 0.0545$

Learn more on confidence interval here: brainly.com/question/15712887