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Olenka [21]
2 years 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]2 years ago
7 0

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

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