Significance Tests for Means

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What is a significance test?

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A significance test is a statistical method used to determine if there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis.

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What is a null hypothesis (H0)?

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The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption in significance testing.

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What is an alternative hypothesis (Ha)?

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The alternative hypothesis (Ha) is a statement that indicates the presence of an effect or a difference, opposing the null hypothesis.

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What does a p-value represent?

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A p-value represents the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true.

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What does it mean to reject the null hypothesis?

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Rejecting the null hypothesis means that there is sufficient evidence to support the alternative hypothesis.

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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 support the alternative hypothesis.

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What is the significance level (α)?

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The significance level (α) is the threshold for determining whether to reject the null hypothesis, commonly set at 0.05.

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What is a one-tailed test?

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A one-tailed test is a significance test that evaluates the probability of the effect in one direction (either greater than or less than a certain value).

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What is a two-tailed test?

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A two-tailed test is a significance test that evaluates the probability of the effect in both directions (either greater than or less than a certain value).

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What is the critical value in hypothesis testing?

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The critical value is the threshold that the test statistic must exceed in order to reject the null hypothesis.