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Hypothesis Testing of Single Mean and Single Proportion: Summary of the Hypothesis Test

Module by: Dr. Barbara Illowsky, Susan Dean

The hypothesis test itself has an established process. This can be summarized as follows:

  1. Determine HoHo and HaHa. Remember, they are contradictory.
  2. Determine the random variable.
  3. Determine the distribution for the test.
  4. Draw a graph, calculate the test statistic, and use the test statistic to calculate the p-value. (A z-score and a t-score are examples of test statistics.)
  5. Compare the preconceived αα with the p-value, make a decision (reject or cannot reject HoHo), and write a clear conclusion using English sentences.

Notice that in performing the hypothesis test, you use αα and not ββ. ββ is needed to help determine the sample size of the data that is used in calculating the p-value. Remember that the quantity 1-β1-β is called the Power of the Test. A high power is desirable. If the power is too low, statisticians typically increase the sample size while keeping αα the same. If the power is low, the null hypothesis might not be rejected when it should be.

Glossary

Hypothesis Testing:
Based on sample evidence procedure to determine whether the hypothesis stated is a reasonable statement and cannot be rejected, or is unreasonable and should be rejected.
p-value:
The probability that event will happen purely by chance assuming the null hypothesis is true. The smaller p-value, the stronger the evidence is against the null hypothesis.

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