Selecting Between One-Tailed and Two-Tailed Hypotheses in Hypothesis Testing

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Hypothesis testing is a statistical method used to make inferences about population parameters based on a sample of data. One-tailed and two-tailed tests refer to the directionality of the hypothesis being tested.

I. One-Tailed Test:

1. Definition:

• In a one-tailed test, the hypothesis is directional and specifies the expected outcome in only one direction (either greater than or less than).
• It is used when the researcher is interested in determining whether a parameter is significantly greater or less than a certain value.

2. Hypotheses:

• Null Hypothesis (H0​): Often denoted as H0​:μ=μ0​ or H0​:σ=σ0​, where μ or σ is the population mean or standard deviation, and μ0​ or σ0​ is the hypothesized value.
• Alternative Hypothesis (H1​ or Ha​): H1​:μ>μ0​ or H1​:μ<μ0​, or similarly for standard deviation.

3. Critical Region:

• The critical region is located entirely in one tail of the distribution.
• The decision to reject the null hypothesis is made if the test statistic falls in this critical region.

4. Decision Rule: