Question

    In hypothesis testing, what does a p-value less than

    0.05 typically indicate?
    A The null hypothesis is proven to be true Correct Answer Incorrect Answer
    B The sample size was too small to draw meaningful conclusions. Correct Answer Incorrect Answer
    C There is strong evidence against the null hypothesis, favoring the alternative hypothesis. Correct Answer Incorrect Answer
    D The confidence interval is too narrow to include the true population parameter. Correct Answer Incorrect Answer
    E The data is not sufficient to reject the null hypothesis. Correct Answer Incorrect Answer

    Solution

    Explanation: A p-value less than 0.05 signifies that the probability of observing the test statistic, or something more extreme, under the null hypothesis is less than 5%. This threshold, commonly used in hypothesis testing, indicates strong evidence against the null hypothesis, prompting its rejection in favor of the alternative hypothesis. It is a measure of the strength of evidence, not absolute proof. This approach underpins statistical decision-making across fields, providing a rigorous standard for hypothesis evaluation. Option A: A p-value does not prove the null hypothesis; it measures evidence against it. Option B: Sample size affects power, but p-value interpretation does not inherently reflect sample size issues. Option D: Confidence intervals are separate from p-values and serve to estimate population parameters. Option E: A p-value below 0.05 typically indicates sufficient evidence to reject the null hypothesis.

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