Illuminating Statistical Analysis Using Scenarios and Simulations

24Homing in on the Population Mean III

Statistical Scenario—-Values

Again, say your sample mean is 4.15 and your sample variance is 1.0.

Could the true community mean be 4.0 or less?

What is the -value?

In the previous lesson, we used a confidence interval to justify not rejecting the null hypothesis. If we want to be more specific than “we cannot rule it out at the 95% confidence level” we can calculate a -value.

Just as constructing confidence intervals for means is analogous to what we did for proportions, deriving -values for means is analogous to what we did for proportions.

Eyeballing our previous histogram, reproduced in Figure 24.1, we can add up the frequencies of all the sample means less than or equal to 4. It looks to be about 70 total. Two-tailed, it is 140. Dividing by 1000 to get relative frequency, we get 0.14. That is our rough approximation for the two-tail -value, which reflects the probability of the population mean being 0.15 or more away from 4.15 on ...