Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:
(8.34%, 17.66%).
What is a confidence interval of proportions?
A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
- [tex]\pi[/tex] is the sample proportion.
- z is the critical value.
- n is the sample size.
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
For this problem, the estimate and the sample size are given, respectively, by:
[tex]\pi = 0.13, n = 200[/tex]
Hence the bounds of the interval are:
- [tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 - 1.96\sqrt{\frac{0.13(0.87)}{200}} = 0.0834[/tex]
- [tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 + 1.96\sqrt{\frac{0.13(0.87)}{200}} = 0.1766[/tex]
As a percentage, the interval is:
(8.34%, 17.66%).
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
