## Point Estimates

- 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.

## Interval Estimates

- 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.

### Example 1:

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?

### Example 2:

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.

### Example 3:

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?

### Variables

**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

**XBar****Bar**: The grand average of the subgroup averages. AKA

- X-bar bar
- X-double bar

Also see types of statistics.