Point and Interval Estimation

Photo by torbakhopper
Photo by torbakhopper

Photo by torbakhopper

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?

point and interval ex 1 chart point and interval ex 1

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.

point and interval ex 2


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?

point and interval ex 3



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.




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