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
You use Z-tables, pretty surprised you didn’t find anything, as you literally just need to good the formula for a confidence interval……. nerdy judgemental stare…
What you do is luck up the z-score in a z-table for the 95% percentile (check your text book on that). *hint* it’s a number around ~~1.5-1.6~~ 1.2-1.3. As I was reminded – this is a *double sided* score. I always screw that up.
you take your sample mean, plus or minus the z-score multiplied by the (sample SD) / (square-root sample size)
I think the challenge to this math problem isn’t the formula, it might be finding the values you don’t know based on the 90% interval and then reusing them for the 95% calculation.
For example, you didn’t mention you knew the sample size. The sample mean is just in the middle of the interval you have, so that’s the sample mean. The 90% Z-score can also be found in a table. So you can calculate the sample size based on the 90% and then use that for your 95% problem.
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]
Latest Answers