Determine a preferably small upper limit for n with a confidence level of 9/(10).

Felix Cohen

Felix Cohen

Answered question

2022-09-05

Determine a preferably small upper limit for n with a confidence level of 9 10 .

Answer & Explanation

Sanaa Holder

Sanaa Holder

Beginner2022-09-06Added 20 answers

Step 1
If they are numbered 0 to n, that's n + 1 numbers so there's one missing. To make the problem nicer, I'll suppose they are numbered 1 to n.
A statistic L is an upper limit for n with confidence level p if for every possible n, P ( L n ) p . In this case if M is the maximum number observed and L = c M where c > 1 is a constant,
P ( L n ) = P ( M n c ) = 1 ( n c 1 n ) 10 1 1 c 10
To make the right side 9 10 , we want to take c = 10 1 / 10 . Thus for the observed M = 100 we would have L≈125.89 L 125.89 , which could be rounded down to 125.

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