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What is the null hypothesis (H0)?

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The null hypothesis (H0) is a statement that there is no effect or no difference, and it is the hypothesis that researchers aim to test against. It is often formulated as H0: μ = k, where μ is the population mean and k is a specific value.

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What is the alternative hypothesis (Ha)?

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The alternative hypothesis (Ha) is a statement that indicates the presence of an effect or a difference. It is what researchers want to prove. For example, Ha: μ > k suggests that the population mean is greater than a specific value.

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What does a p-value represent in hypothesis testing?

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A p-value represents the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. A low p-value indicates strong evidence against the null hypothesis.

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What is the significance level (α) in hypothesis testing?

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The significance level (α) is the threshold for determining whether to reject the null hypothesis. Common values are 0.05 and 0.01, indicating a 5% or 1% risk of concluding that a difference exists when there is none.

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What does it mean to reject the null hypothesis?

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To reject the null hypothesis means that the evidence from the data is strong enough to conclude that the null hypothesis is unlikely to be true, suggesting that there is a significant effect or difference.

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What does it mean to fail to reject the null hypothesis?

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Failing to reject the null hypothesis means that there is not enough evidence to conclude that the null hypothesis is false. It does not prove that the null hypothesis is true.

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What is a one-tailed test?

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A one-tailed test is a hypothesis test in which the alternative hypothesis specifies a direction of the effect (e.g., Ha: μ > k or Ha: μ < k). It tests for the possibility of the relationship in one direction.

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What is a two-tailed test?

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A two-tailed test is a hypothesis test in which the alternative hypothesis does not specify a direction (e.g., Ha: μ ≠ k). It tests for the possibility of the relationship in both directions.

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What is the formula for the t-test statistic?

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What is the degrees of freedom (df) in a t-test?

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