Hypothesis Testing - Intro to Proportions

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What is a hypothesis test?

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A hypothesis test is a statistical method used to make decisions about a population parameter based on sample data. It involves formulating a null hypothesis (H₀) and an alternative hypothesis (Hₐ), then using sample data to determine whether to reject H₀.

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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, opposing the null hypothesis.

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What does a right-tailed test indicate?

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A right-tailed test is used when the alternative hypothesis (Hₐ) states that the parameter is greater than a certain value (e.g., Hₐ: p > 15).

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What distribution is used for hypothesis testing about population proportions?

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The z-distribution is used for hypothesis testing about population proportions.

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

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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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How do you determine the critical value for a left-tailed test?

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The critical value for a left-tailed test can be found using z-tables or statistical software, based on the significance level (α). For α = 0.05, the critical value is z₀ = -1.645.

Tags

CCSS.HSS.ID.A.4

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What is the purpose of a p-value in hypothesis testing?

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The p-value measures the strength of evidence against the null hypothesis. A small p-value (typically ≤ α) indicates strong evidence to reject H₀.

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What does it mean if the p-value is less than the significance level (α)?

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If the p-value is less than α, it suggests that the sample data provides sufficient evidence to reject the null hypothesis.

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What is a two-tailed test?

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A two-tailed test is used when the alternative hypothesis (Hₐ) states that the parameter is different from a certain value (e.g., Hₐ: p ≠ 0.50).