Confidence Interval Behavior and Sample Size. Presentation 7.2. Structure of the Confidence Interval. Margin of Error. The standard deviation of the estimate. An estimate for μ from your sample. Based on level of confidence, how many standard deviations away you can tolerate.
Margin of Error
The standard deviation of the estimate.
An estimate for μ from your sample
Based on level of confidence, how many standard deviations away you can tolerate
4.8 – 4.2 = 0.6
It must be in the middle, so 4.5.
You must be adding / subtracting 0.3 from 4.5 to get the interval, so the margin of error is 0.3.
Earlier we obtained a confidence interval
for the mean fuel capacity of a certain
model of car. In that example, we were
given the sample size of 40. This time,
suppose that we want to obtain a 90%
confidence interval for μ and σ and we
want the margin of error to be 0.2.
This is the margin of error (E) and we want it to be 0.2. After you substitute everything that you know into the equation, solve for n.
This means we need at least a sample of size 829 to achieve this margin of error.
Here, you have to estimate p-hat from a smaller sample size, perhaps a pilot study. In most cases, 0.5 is used in place of p-hat because this is the worst case scenario (generates the largest error that might be expected).