- A statistic (value obtained from sample) is used to estimate a parameter (value from the population).
- Take a sample, find x bar. X bar is a close approximation of μ
- Depending on the size of your sample that may not be a good point estimate.
- s is a good approximation of σ
- If we want stronger confidence in what range our estimate lies, we need to do a confidence interval.
- Broader and probably more accurate than a point estimate
- Used with inferential statistics to develop a confidence interval – where we believe with a certain degree of confidence that the population parameter lies.
- Any parameter estimate that is based on a sample statistic has some amount of sampling error.
A large company conducted a series of tests to determine how much data individual users were storing on the file server. A random sample of 15 users revealed an average 15.32 GB with a standard deviation of 0.18 GB. What is the interval that contains the actual company user average?
A plastic injection molding company is trying out a new die. Based on a sample of 25 trials, the average cycle time was 7.49 seconds with a standard deviation of 0.22 seconds. However, this machine has been used for similar jobs before and has a known process variance of 0.0576. Find the confidence limits of µ. Test at the 99% confidence level.
25 parts are randomly selected from a plastic injection molding process and their lengths are measured. The mean length of the 25 parts is 4.32 cm with a standard deviation of 0.17 cm. What is the 95% confidence interval for the actual mean of this process?
s (or sd): The sample standard deviation is a point estimate for the population standard deviation / the dispersion statistic for samples
µ: the central tendency statistic for populations
XBar: a point estimate for the population mean
σ: the actual population standard deviation / symbol for the measurement of dispersion in a population
N is for populations
n: The statistic for number of data in a sample
x: the individual value
XBarBar: The grand average of the subgroup averages. AKA
- X-bar bar
- X-double bar
Also see types of statistics.