This proposes a range of plausible values for an unknown parameter. The interval has an associated confidence level that the true parameter is in the proposed range.
Then you can use the mean of their heights (Estimated Mean) to estimate the average heights in the state (True Mean).
We cast a net from the value we know .
To get such ranges or intervals, we go
1.96 SD away from (the sample mean) in both directions. And this range is the
95% confidence interval.
Now, when we say that, we estimate the true mean to be (the sample mean) with a confidence interval of [ ], we are literally saying that: It is with
95% probability that the true population mean is within these Confidence Interval limits.
When you take 99% CI, you essentially increase the proportion and thus cast a wider net with three standard deviations.
Here, is the sample mean (mean of the 1000 heights sample we took). is the no. of standard deviations away from the sample mean (1.96 for 95%, 2.576 for 99%), level of confidence we want. is the standard deviation in the sample. is the size of the sample.