9709 · 6.5
Hypothesis tests flashcards
Revision flashcards for Cambridge 9709 Hypothesis tests (syllabus 6.5). Flip, recall, then mark a real past-paper question.
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What is a null hypothesis, $H_0$?
The default assumption or statement of 'no effect' or 'no change' about a population parameter. It always contains an equality sign (e.g., $\mu = 10$, $p = 0.4$).
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What is an alternative hypothesis, $H_1$?
The statement that contradicts the null hypothesis, suggesting a change, difference, or effect. It contains an inequality (e.g., $\mu > 10$, $\mu \neq 10$, $p < 0.4$).
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What is a significance level, $\alpha$?
The probability of rejecting the null hypothesis when it is actually true (a Type I error). Common values are 10%, 5%, and 1%. It defines the threshold for 'strong evidence'.
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What is a critical region?
The set of values for the test statistic that would lead to the rejection of the null hypothesis. The size of this region is determined by the significance level, $\alpha$.
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What is a test statistic?
A value calculated from sample data that is used to decide whether to reject the null hypothesis. It measures how many standard errors the sample statistic is from the hypothesised population parameter.
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When do you use a one-tailed test?
When the alternative hypothesis specifies a direction of change, using words like 'increase', 'decrease', 'greater than', or 'less than'. For example, $H_1: \mu > 50$.
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When do you use a two-tailed test?
When the alternative hypothesis does not specify a direction, using words like 'changed', 'different from', or 'not equal to'. For example, $H_1: p \neq 0.25$.
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What is a Type I error?
Rejecting a true null hypothesis. It's a 'false positive'. The probability of a Type I error is equal to the significance level, $\alpha$.
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What is a Type II error?
Failing to reject a false null hypothesis. It's a 'false negative'. Its probability is denoted by $\beta$.
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What is a p-value?
The probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming the null hypothesis is true. If $p < \alpha$, we reject $H_0$.
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How do you conclude a hypothesis test?
First, state whether you reject or do not reject $H_0$ based on the comparison. Second, write a concluding sentence in the context of the original problem, explaining what your decision means.