9.9 Hypothesis testing of single mean and single proportion:

• In a hypothesis test problem, you may see words such as "the level of significance is 1%." The "1%" is the preconceived or preset $\alpha$ .
• The statistician setting up the hypothesis test selects the value of $\alpha$ to use before collecting the sample data.
• If no level of significance is given, the accepted standard is to use $\alpha =0.05$ .
• 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 thehypothesis test left, right, or two tailed.
• The alternate hypothesis , $H_a$ , tells you if the test is left, right, or two-tailed. It is the key to conducting the appropriate test.
• $H_a$ 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.