Confidence Interval for a Single Mean

confidence interval for a single mean, specifically, is just a regular confidence interval that tries to estimate the possible mean of the population. Stattrek explains a confidence interval as “…to describe the amount of uncertainty associated with a sample estimate of a population parameter.”It’s not exact, and the higher percentage of confidence you want, the bigger the interval will become.

It is useful for predicting the interval in which the true mean will likely reside.

This is the process of going through this specific confidence interval:

1. Check your conditions

  • random- Is your sample random and a good representation of the entire population?
  • 10%- Is your sample ten percent or less than your population?
  • nearly normal- Is your sample normally distributed? It is easy to check for this in SPSS if you were to look at the Q-Q plots of the data. If the dots are pretty close to the line and there are no apparent outliers then you are good.
  • n≥40- If your sample is around forty or bigger then there is no need to check if it is nearly normal.

2. Calculation

  • \overline{y}– This is the sample mean.
  • t^*_{df}\left(\frac{s}{\sqrt{n}}\right)– This is the margin of error. The t depends on the degrees of freedom, which is the sample size n minus one.
  • interval: \left(\overline{y}-t^*_{df}\left(\frac{s}{\sqrt{n}}\right),\overline{y}+t^*_{df}\left(\frac{s}{\sqrt{n}}\right)\right)

3. Conclusion

  • This will say something along the lines of “We are _____ % confident that the true population mean is captured in this interval.”


The t in step two is not easy to calculate and the use of SPSS will be needed as it changes from test to test. Here is a site that helps to understand confidence intervals in general and, if you do not see the “demo” button, this is a link to test out a confidence integral. Unless you sign in, you will not be able to use the full version. The demo lets you explore sample populations up to 150. There will be a place to  specify the interval to a single mean. This is an one example for the confidence interval and this is another example that is more in depth and also has instructions for using minitab.


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