Please explain every single detail! Would really love to learn it. Thank you! (P
ID: 3220834 • Letter: P
Question
Please explain every single detail! Would really love to learn it. Thank you! (Please solve too)
Milton Mathematics heard the following two reports on the radio yesterday:
Report 1: Most Mathematicians are Magicians
One study found that 54% of Mathematicians have an interest in magic. ... This study has a margin of error of 3%.
Report 2: Is there a Connection between Mathematics and Magic?
One study found that 54% of Mathematicians have an interest in magic. ... This study has a margin of error of 6%.
Create confidence intervals for each of these reports.
Interpret these confidence intervals, noting any missing information.
Milton believes that these two reports cannot possible be about the same study. Explain how these two reports could be about the same study. Make sure that your explanation includes what information that the radio announcers left out of their on-air reports.
Based on these reports about this study, what claims can we make about the population of mathematicians and their interest in magic? How confident (in terms of a percentage) are you in your claims?
Explanation / Answer
margin of error, moe = z*sqrt (p(1-p)/n),
z is the critical value at 95% Confidence level, z = 1.96
p = 54%, moe = 3% for report 1
n = (z/moe)^2 * p(1-p)
n = 1060 when moe = 3%
n = 265 when moe = 6%
The CI (confidence intervals) when moe =3% is (51%, 57%) at 95% confidence levels
The CI (confidence intervals) when moe =6% is (48%, 60%) at 95% confidence levels
Meaning - We can say that the proportion of mathematicians who have an interest in magic will be within 51% to 57% with 95% confidence levels. This will have a margin of error to be within 3% for report1
It is absolutely possible that the margin of error can be 3% or 6%.
What is really missing of the two reports is the confidence level, alpha. Because for our calculations we have assumed it as 95%. If it is 90% the sample size would be different.
We are 95% confident that the proportion of mathematicians interested in magic are 48% and 60% (because we want the margin of error to be liberal).
moe p N=(z/moe)^2 *p(1-p) Lower CI Upper CI 3% 54% 1,060 51% 57% 6% 54% 265 48% 60%