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    Question

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

    0.05 typically indicate ?
    A The null hypothesis is accepted with high confidence. Correct Answer Incorrect Answer
    B There is a high probability that the null hypothesis is true. Correct Answer Incorrect Answer
    C The null hypothesis is rejected, and there is evidence supporting the alternative hypothesis. Correct Answer Incorrect Answer
    D The result is statistically insignificant. Correct Answer Incorrect Answer
    E The test needs to be repeated with a larger sample size. Correct Answer Incorrect Answer

    Solution

    Explanation: A p-value less than 0.05 typically indicates that the observed results are unlikely to occur under the null hypothesis. This threshold suggests that there is less than a 5% probability that the results are due to random chance, leading researchers to reject the null hypothesis in favor of the alternative. For example, in a t-test comparing means, a p-value < 0.05 would imply a significant difference between groups. However, it does not measure the magnitude of the effect or its practical significance, which requires further evaluation. Option A: A low p-value leads to the rejection of the null hypothesis, not its acceptance. Option B: The p-value does not represent the probability of the null hypothesis being true; it indicates the likelihood of the observed result under the null. Option D: A p-value < 0.05 signifies statistical significance, not insignificance. Option E: Sample size considerations are separate from interpreting p-values and do not affect the threshold for significance.

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