P-Values (Leaving Cert Mathematics): Quizzes

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What does a p-value represent in hypothesis testing?

Probability of data as extreme, if H0H_0 true

What does the null hypothesis (H0H_0) state?

There is no effect or no difference

What does the alternative hypothesis (H1H_1) represent?

A statement contradicting H0H_0

If p<αp < \alpha, what is the correct decision?

Reject H0H_0, strong evidence against it

If p≥αp \geq \alpha, what does this indicate?

Weak evidence against H0H_0, not rejected

What are common significance levels (α\alpha) used?

0.05 or 0.01

What is the first step in hypothesis testing?

Formulate H0H_0 and H1H_1

In Example 1, with p=0.0226p = 0.0226 and α=0.05\alpha = 0.05, what is the decision?

Reject H0H_0

In Example 2, with p=0.08p = 0.08 and α=0.05\alpha = 0.05, what is the conclusion?

Fail to reject H0H_0, insufficient evidence

What does the p-value measure, assuming H0H_0 is true?

Probability of observing data as extreme

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