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I read that in this post here (Confidence interval without std?), it is possible to calculate Confidence Intervals for a Proportion without explicitly knowing the Standard Deviation.

  • But can this idea also be extended to basic averages?

For example, suppose my friend randomly measures the height of 100 students in a university, and the population of the university is 1000 students. He ONLY tells me that the average height of these 100 students that he measured is 163 cm. He also tells me how many students he measured and how many students are there at the university.

Solely based in this information, can some application of the Central Limit Theorem (CLT; https://en.wikipedia.org/wiki/Central_limit_theorem) be used to construct some sort of generic confidence interval on this average height (163 cm) ? Or does doing so explicitly require you to have knowledge of the Standard Deviation?

Thanks!

RobPratt
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stats_noob
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    Without further information, no. The problem is that you don't have enough information about the underlying distribution. Intuitively, you can't distinguish between a situation where everyone in the school has a height of exactly 163 cm vs. a situation where the population distribution has a large standard deviation. – angryavian Sep 04 '22 at 17:29
  • @ angryavian: thank you for your answer! this was the kind of logic that I was thinking, but I wasn't sure if I was correct. I guess you could have re-structured this question and asked your friend to record whether each of these 100 students were taller than 163 cm (yes/no) - and then, you could have found out the proportion and the confidence interval on the proportion of students who were taller than 163 cm .... without explicitly knowing the standard deviation? thank you so much! – stats_noob Sep 04 '22 at 17:32

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