Correct statement related to confidence interval

AI Thread Summary
The discussion centers on the misunderstanding of confidence intervals and the nature of the proportion p, which represents a fixed value rather than a random variable. Participants clarify that statements implying p has a probability associated with it are incorrect, as p is not subject to variability. The confusion arises particularly between options (a) to (d), with one user questioning if only option (a) is correct. Emphasis is placed on the importance of using the term "confidence" to express belief strength, rather than suggesting a percentage chance. Overall, the conversation highlights the need for clarity in statistical terminology and concepts.
songoku
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Homework Statement
A student was asked to find a 99% confidence interval for the proportion of students who are left-handed using data of randomly chosen 80 students. Which of the following is the correct interpretation of interval 0.20 < p < 0.40? You may choose more than one option
a) With 99% confidence, the proportion of all students who are left-handed is between 0.20 and 0.40
b) There is a 99% chance that the proportion of the population is between 0.20 and 0.40
c) There is a 99% chance that the proportion of left-handed students in a sample of 80 students will be between 0.20 and 0.40
d) The proportion of all students who are left-handed is between 0.20 and 0.40, 99% of the time
e) With 99% confidence, a randomly selected student who are left-handed in the proportion of their classes that is between 0.20 and 0.40
Relevant Equations
None
I think (e) is wrong because the proportion should be out of the whole population, not only in a certain class and option (a) to (d) looks like identical to me so I answered (a), (b), (c) and (d) but my answer is wrong.

Where is my mistake? Thanks
 
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Remember that p represents a single value, the proportion of students who are left-handed. That is not a random variable. So rule out any statement that talks as though it is a random variable with a probability.
 
FactChecker said:
Remember that p represents a single value, the proportion of students who are left-handed. That is not a random variable. So rule out any statement that talks as though it is a random variable with a probability.
I understand your hint but I seem can't tell the difference between options (a) to (d). Is the correct answer only (a)?

Thanks
 
Be very skeptical of anything that says "99% chance" or "99% of the time". That might imply that p is a random variable rather than a fixed number. As a single fixed number, it always is or it always isn't. There is no "% chance" or "% of the time". That is why statisticians like to use the word "confidence". It indicates their strength of belief rather than implying that p is a random variable.
 
Thank you very much FactChecker
 

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