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P-Value and Critical Value Comparison

Move the slider for μ to change the population mean.
Move the slider for σ to change the population standard deviation.
Move the confidence/α slider to change the confidence and significance.
Move the slider for size to change the sample size.
Move the type slider to select the test type: left-tailed, right-tailed, two-tailed.

Finally, move the slider for seed to generate a new random sample.
See how the hypothesis test results from the critical value approach
and from the P-value approach compare.

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The critical value approach and the P-value approach give the same results when testing hypotheses. The P-value approach has the advantage in that you just need to compute one value, the P-value, to do the test. For the critical value approach, you need to compute the test statistic and find the critical value corresponding to the given confidence or significance level. Because the P-value approach requires just one computation, most statistical software and calculators use the P-value approach for hypothesis testing.

The critical value is the standard score such that the area in the tail on the opposite side of the critical value (or values) from zero equals the corresponding significance level, α . The P-value is the probability of obtaining a test statistic as extreme as the one for the current sample under the assumption that the null hypothesis is true.

David Gurney, Created with GeoGebra