Significance Tests for Means

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What is a null hypothesis (H₀)?

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

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What is an alternative hypothesis (Hₐ)?

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An 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 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 a significance level (α)?

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The significance level (α) is the probability of rejecting the null hypothesis when it is actually true, commonly set at 0.05 or 0.01.

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What is a p-value?

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

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What does a p-value less than α indicate?

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A p-value less than α indicates that the results are statistically significant, leading to the rejection of the null hypothesis.

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What is a one-tailed test?

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A one-tailed test is a hypothesis test that evaluates the direction of the effect, 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 hypothesis test that evaluates whether a parameter is significantly different from a certain value, without specifying a direction.

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What is the formula for the z-test statistic?

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The formula for the z-test statistic is z = (x̄ - μ) / (σ/√n), where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.