# Confidence Intervals Tricky Question

• Jun 25th 2012, 08:45 AM
u12480
Confidence Intervals Tricky Question
Can you please explain to me you the numbers in denoted in the confidence intervals derived?
• Jun 25th 2012, 09:41 AM
biffboy
Re: Confidence Intervals Tricky Question
For example when getting a 95% confidence interval for the mean we use 1.96 because in a normal distribution 95% of the values lie in the interval from 1.96 standard deviations below the mean to 1.96 standard deviations above the mean.
• Jun 25th 2012, 09:54 AM
u12480
Re: Confidence Intervals Tricky Question
Do you know where they 1.96 initially came from? The question in my book acknowledges all of the percentiles with the confidence intervals but specifically asks how these numbers (1.645, 1.96, 2.33, 2.567) were selected.
• Jun 25th 2012, 01:42 PM
pickslides
Re: Confidence Intervals Tricky Question
They come from the normal distribution as explained in post #2.

Have a look here Z table - Normal Distribution

You should find that 1.645 is the 90th percentile, 1.96 the 95th, 2.33 the 98th, 2.567 the 99th percentile
• Jun 25th 2012, 01:53 PM
u12480
Re: Confidence Intervals Tricky Question
Hello:
Yes, I understand exactly what you are saying but the question wants to know where those numbers originated when the equation was being developed in the original development of this equation. In other words, how did the founder of the equation decide on those particular numbers? Sounds like a crazy question but it's the one I've been given.
• Jun 25th 2012, 02:10 PM
HallsofIvy
Re: Confidence Intervals Tricky Question
You have been told that repeatedly! The "1.96" is the value such that, with "z" being a "standard normal" random variable, the probability that z< 1.96 is .95.
• Jun 26th 2012, 03:11 AM
u12480
Re: Confidence Intervals Tricky Question
I'm sorry that it appears I don't understand. I know what you're saying exactly but the question wants to know how these numbers were originally selected by the person who made up this equation. Were the numbers pulled out of the air or were they based on something? It's more a history question I think than math.
• Jun 26th 2012, 02:26 PM
pickslides
Re: Confidence Intervals Tricky Question
Sounds like it
• Jun 26th 2012, 10:17 PM