Correct statement related to confidence interval

[songoku]

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

 

[FactChecker]

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.

 

[songoku]

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

 

[FactChecker]

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.

 

[songoku]

Thank you very much FactChecker