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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 hypothesis 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, and it is what the researcher aims to support.

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How do you state a null and alternative hypothesis for a mean test?

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For a mean test, the null hypothesis is typically stated as H₀: μ = μ₀ (where μ₀ is the hypothesized mean), and the alternative hypothesis can be Hₐ: μ > μ₀, Hₐ: μ < μ₀, or Hₐ: μ ≠ μ₀ depending on the research question.

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What is a one-sample z-test?

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A one-sample z-test is a statistical test used to determine whether the mean of a single sample is significantly different from a known population mean.

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What is the formula for the z-test statistic?

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Tags

CCSS.HSS.ID.A.4

Front

What does a p-value represent in hypothesis testing?

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

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The significance level (α) is the threshold for rejecting the null hypothesis, commonly set at 0.05 or 0.01.

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What does it mean if the p-value is less than α?

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If the p-value is less than α, it indicates that the observed data is statistically significant, leading to the rejection of the null hypothesis.

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What is a Type I error?

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A Type I error occurs when the null hypothesis is incorrectly rejected when it is actually true.

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What is a Type II error?

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A Type II error occurs when the null hypothesis is not rejected when it is actually false.