We are given a 95\% confidence interval with some range

windpipe33u

windpipe33u

Answered question

2022-04-21

We are given a 95% confidence interval with some range - in this particular case (4.0; 11.0) - to find the 90% and 99% confidence intervals for the same parameter, assuming normal distribution, without any aditional information.

Answer & Explanation

impire7vw

impire7vw

Beginner2022-04-22Added 19 answers

Step 1
Based on your formulae x±t×sx, it seems like you are dealing with a t confidence interval. If so, you will need the sample size n to accurately get the 90% or 99% confidence interval.
But, just to clarify the thought process, suppose the 95% confidence interval given (4,11) is a z confidence interval. If so, you can get the other confidence intervals based on the following logic (some of which also apply in the t confidence interval scenario as well).
First, the mid-point of that interval is the sample mean x by design. So
x=4+112=7.5
Second, the half-length of the interval is 1.96×σn
So σn=(117.5)1.96=3.51.96
Then, 90% confidence interval:
x±1.645×σn7.5±1.645×3.51.96

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