Introduction to Hypothesis Testing: 20 flashcards
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1. What is hypothesis testing?
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A formal procedure for deciding whether sample evidence is strong enough to reject a claim about a population parameter.
2. What does the null hypothesis ($H_0$) always contain?
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An equality, such as $\mu = \mu_0$ or $p = p_0$.
3. What does the alternative hypothesis ($H_a$) express?
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What the researcher suspects is true — a difference or effect that contradicts $H_0$.
4. What is the significance level $\alpha$?
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The threshold probability for rejecting $H_0$, commonly 0.05.
5. What is a test statistic?
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A standardized measure of how far the sample is from what $H_0$ predicts.
6. What is the p-value?
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The probability of a result at least as extreme as observed, assuming $H_0$ is true.
7. When do you reject $H_0$ using the p-value approach?
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When $p < \alpha$.
8. When do you reject $H_0$ using the critical-value approach?
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When the test statistic falls in the rejection region beyond the critical value.
9. What is a Type I error?
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Rejecting a true $H_0$; its probability is $\alpha$.
10. What is a Type II error?
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Failing to reject a false $H_0$; its probability is $\beta$.
11. What is power in hypothesis testing?
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$1 - \beta$, the probability of correctly rejecting a false $H_0$.
12. How does decreasing $\alpha$ affect Type II error for fixed $n$?
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It increases $\beta$ — the two errors trade off.
13. How can you reduce both Type I and Type II error probabilities?
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By increasing the sample size $n$.
14. How does a two-tailed test split $\alpha$?
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It splits $\alpha$ across both tails, so each tail gets $\alpha/2$.
15. How does a one-tailed test allocate $\alpha$?
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It puts all of $\alpha$ in one direction, the direction of the alternative.
16. What does failing to reject $H_0$ mean?
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There is insufficient evidence to reject $H_0$ — it does not prove $H_0$ is true.
17. Does statistical significance imply practical importance?
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No — large samples can make tiny, unimportant effects statistically significant.
18. What is the one-sample z-test formula?
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$$z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}}$$
19. In which fields is hypothesis testing used?
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Clinical trials, quality control, and A/B testing, among others.
20. What is the correct phrasing when $p \geq \alpha$?
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"There is insufficient evidence to reject $H_0$ at the $\alpha$ level."
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