Calculate confidence level from a given confidence interval. I'm fairly comfortable calculating the confidence interval. But now I'm seeing a problem where I'm giving a confidence interval CI(27.6621,30.3379) and I'm requested to calculate the confidence level.

Melina Barber

Melina Barber

Answered question

2022-09-21

Calculate confidence level from a given confidence interval
I'm fairly comfortable calculating the confidence interval. But now I'm seeing a problem where I'm giving a confidence interval CI(27.6621,30.3379) and I'm requested to calculate the confidence level. I'm also given the sample size n = 85 and a standard deviation σ = 7.5. I can't find a formula for that, I feel like it's something simple I'm not seeing. Any help would be appreciated.

Answer & Explanation

Carina Moon

Carina Moon

Beginner2022-09-22Added 6 answers

Step 1
Assuming that the data comes from N ( μ , σ 2 ) with known σ 2 , we have that
n ( X ¯ n μ ) σ N ( 0 , 1 ) .
If z 1 α is such that P ( N ( 0 , 1 ) z α / 2 ) = α / 2, then the CI for μ is
( X ¯ n σ n z α / 2 , X ¯ n + σ n z α / 2 ) .
Step 2
Substract both sides to get that
2 σ n z α / 2 = c ,,
where c is known. In a normal table find the α such that z α / 2 = c n / ( 2 σ )

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?