# Correct statement related to confidence interval

• songoku
In summary, the conversation is discussing the correct answer to a question about the use of a proportion in statistics. The correct answer is option (a) because it is the only option that does not imply that the proportion is a random variable. The hint given is to be skeptical of any statement that uses words like "chance" or "time" when referring to the proportion. Instead, statisticians prefer to use the term "confidence" to indicate their level of belief in the proportion.

#### 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

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
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.

songoku
Thank you very much FactChecker