Hypothesis Testing Concepts

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What is a null hypothesis?

Back

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?

Back

The alternative hypothesis (H1) is a statement that indicates the presence of an effect or a difference, opposing the null hypothesis.

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Can the null and alternative hypothesis be the same?

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No, the null and alternative hypotheses must be distinct; they represent opposing statements.

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What does it mean if a sample mean is in the critical region?

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If a sample mean is in the critical region, it suggests that the null hypothesis can be rejected at the specified alpha level.

Tags

CCSS.HSS.IC.B.4

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

Back

The significance level (alpha) 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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If a sample mean is in the critical region at alpha = 0.05, will it always be in the critical region at alpha = 0.01?

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False; a sample mean in the critical region at a higher alpha level may not be in the critical region at a lower alpha level.

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How do you state the null and alternative hypotheses for 'Less than 4% of high school students take Statistics'?

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H0: p = 0.04; H1: p < 0.04.

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If a sample mean is in the critical region at alpha = 0.01, will it always be in the critical region at alpha = 0.05?

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True; a sample mean in the critical region at a lower alpha level will also be in the critical region at a higher alpha level.

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What are the null and alternative hypotheses for the average weight of a 6th grade student's backpack being 18.4 lbs?

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H0: μ = 18.4; H1: μ ≠ 18.4.

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What is a Type I error in hypothesis testing?

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