– changing the confidence interval of a sample?

Question

I know a 90% confidence interval is between [1.527, 1.632] that’s it. And I need to find the limits for a 95% Confidence interval how do you do this?

I only know the limits, that is has a normal distribution and the standard deviation has a value of σ.

I’ve tried looking online and in a textbook and I’ve found NOTHING

In: Mathematics

Answer 1

First you need the midpoint of the confidence interval, this is: (1.527 + 1.632)/2 = 1.5795.

Then you need the standard error. You form a 90% confidence interval by multiplying the standard error by 1.645, then adding and subtracting that from the midpoint. Hence

SE = (1.632 – 1.5795)/1.645 = 0.0319

Finally, you form a 95% confidence interval by multiplying the standard error by 1.96, then adding and subtracting from the midpoint: [1.517, 1.642]