The following examples illustrate a left-, right-, and two-tailed test. This makes the data analyst use judgment rather than mindlessly applying rules. Similarly, for a large p-value such as 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 not rejecting the null hypothesis. 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.
H a never has a symbol that contains an equal sign.It is the key to conducting the appropriate test. The alternative hypothesis, H a, tells you if the test is left, right, or two-tailed.For this reason, we call the hypothesis test left, right, or two tailed. 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.If no level of significance is given, a common standard to use is α = 0.05.The statistician setting up the hypothesis test selects the value of α to use before collecting the sample data.In a hypothesis test problem, you may see words such as “the level of significance is 1%.” The “1%” is the preconceived or preset α.
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