Hypothesis Testing: practice question
Testing H0: μ = 0 against Ha: μ ≠ 0 at the 5% significance level with a large sample, an analyst computes a test statistic of −2.40 and compares it with critical values of ±1.96. The most appropriate conclusion is to:
- reject H0, because −2.40 lies in the rejection region of the two-tailed test
- fail to reject H0, because a negative test statistic cannot be statistically significant
- fail to reject H0, because the p-value of the test exceeds 0.05
Show answer and explanation
Correct answer: A
Explanation: A is correct: for a two-tailed 5% test the rejection region lies below −1.96 or above +1.96, and −2.40 falls below −1.96, equivalently a two-tailed p-value of about 0.0164 is smaller than 0.05. B invents a rule that does not exist — the test compares the statistic's magnitude with the critical value, so negative values can absolutely be significant. C gets the comparison backwards: a statistic this far from zero produces a p-value below, not above, 0.05.
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