Hypothesis Testing

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What is a hypothesis in statistics?

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A hypothesis is a statement or assumption about a population parameter that can be tested using statistical methods.

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What are the null and alternative hypotheses?

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The null hypothesis (H0) is a statement of no effect or no difference, while the alternative hypothesis (Ha) is what you want to prove, indicating an 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 support the alternative hypothesis.

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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 is the significance level (alpha) in hypothesis testing?

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

Tags

CCSS.HSS.IC.B.4

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

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If the p-value is less than alpha, we reject the null hypothesis, indicating that the results are statistically significant.

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What is a Type I error?

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

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What is a Type II error?

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A Type II error occurs when the null hypothesis is false but is incorrectly failed to be rejected.

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What is the first step in conducting a hypothesis test?

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The first step is to state the null and alternative hypotheses.

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How do you interpret a p-value of 0.03 when alpha is set at 0.05?

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Since 0.03 < 0.05, we reject the null hypothesis, suggesting that there is significant evidence for the alternative hypothesis.