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Additional Information

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

  • In a hypothesis test problem, you may see words such as "the level of significance is 1%." The "1%" is the preconceived or preset αα.
  • The statistician setting up the hypothesis test selects the value of αα to use before collecting the sample data.
  • If no level of significance is given, the accepted standard is to use α=0.05α=0.05.
  • When you calculate the p-value and draw the picture, the p-value is the area in the left tail, the right tail, or split evenly between the two tails. For this reason, we call the hypothesis test left, right, or two tailed.
  • The alternate hypothesis, HaHa, tells you if the test is left, right, or two-tailed. It is the key to conducting the appropriate test.
  • HaHa never has a symbol that contains an equal sign.
  • Thinking about the meaning of the p-value: A data analyst (and anyone else) should have more confidence that he made the correct decision to reject the null hypothesis with a smaller p-value (for example, 0.001 as opposed to 0.04) even if using the 0.05 level for alpha. Similarly, for a large p-value like 0.4, as opposed to a p-value of 0.056 (alpha = 0.05 is less than either number), a data analyst should have more confidence that she made the correct decision in failing to reject the null hypothesis. This makes the data analyst use judgment rather than mindlessly applying rules.

The following examples illustrate a left, right, and two-tailed test.

Example 1

H o H o : μμ = 5 =5 H a H a : μμ < 5 <5

Test of a single population mean. HaHa tells you the test is left-tailed. The picture of the p-value is as follows:

Normal distribution curve of a single population mean with a value of 5 on the x-axis and the p-value points to the area on the left tail of the curve.

Example 2

H o H o : pp ≤ 0.2 ≤0.2 H a H a : pp > 0.2 >0.2

This is a test of a single population proportion. HaHa tells you the test is right-tailed. The picture of the p-value is as follows:

Normal distribution curve of a single population proportion with the value of 0.2 on the x-axis. The p-value points to the area on the right tail of the curve.

Example 3

H o H o : μμ = 50 =50 H a H a : μμ ≠ 50 ≠50

This is a test of a single population mean. HaHa tells you the test is two-tailed. The picture of the p-value is as follows.

Normal distribution curve of a single population mean with a value of 50 on the x-axis. The p-value formulas, 1/2(p-value), for a two-tailed test is shown for the areas on the left and right tails of the curve.

Glossary

Hypothesis Testing:
Based on sample evidence, a 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 an event will happen purely by chance assuming the null hypothesis is true. The smaller the p-value, the stronger the evidence is against the null hypothesis.

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Definition of a lens

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A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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