Confidence interval for difference confidence level. Lets say I measure quantity μ and compute confidence interval for it [mu-delta_1, mu+delta_2] with a 68% confidence limit.

Freddy Chaney 2022-09-24 Answered
Confidence interval for difference confidence level
Lets say I measure quantity μ and compute confidence interval for it [ μ δ 1 , μ + δ 2 ] with a 68% confidence limit.
What if I want a confidence interval for 95% CL, can I simply scale errors like this? Let x = 0.95 0.68
[ μ x δ 1 , μ + x δ 2 ]
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Answers (1)

Rachael Conner
Answered 2022-09-25 Author has 8 answers
Step 1
No you can't. This would only be true if your sampling distribution were uniform. When the sampling distribution is Gaussian we have critical values of (approximately) 1 and 2 for 68 % and 95 % so the ratio is larger than you'd predict.
Step 2
This is cause there is less probability density further out. Observe also for a Gaussian (or any sampling distribution with support on the whole real line), the width of a 100% CI would have to be infinite. The relationship between the critical values for the two percentiles is something that depends on the quantities of the sampling distribution and must be derived on a case by case basis.
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