So 2.2+.2068 and 2.2-.2068 give you the interval.
- 12-14-2010, 12:30 PM2forISURe: Help on Confidence Interval and Hypothesis Testing
- 12-14-2010, 12:43 PMedr247Re: Help on Confidence Interval and Hypothesis TestingCyclone North hit it on the head.
1.96 is the Z value that will yield you a 95% interval in a normal distribution (think of the bell curve).
2.2 is the sample mean.
.35 is the standard deviation
(.35/sqrt(11)) will yield you the standard error
So, 2.2 + 1.96*(.35/sqrt(11)) => 2.2 + .2068 => 2.4068. This is the upper limit of your 95% confidence interval.
Similarly, 2.2 - 1.96*(.35/sqrt(11)) => 2.2 - .2068 => 1.9932. This is the lower limit of your 95% confidence interval.
Therefore, your 95% confidence interval can be written as (1.9932, 2.4068), or 1.9932
However, more than simply calculating the CI, you need to interpret it. What these numbers are showing you (especially if you write the answer like 1.9932
- 12-14-2010, 05:48 PMbesserheimerphatRe: Help on Confidence Interval and Hypothesis TestingJust to add to what edr said, increasing the confidence interval will increase the range of the CI limits. In other words, it is more likely that the true mean falls between 1.95 and 2.5. It's even more likely that the true mean falls between 1.9 and 2.6. You have more confidence (higher CI) that the true mean falls within an expanded range. Holding everything else the same, as you decrease your confidence interval the upper and lower limits converge on the mean.