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    Question

    Which of the following statements best describes the

    purpose of a p-value in hypothesis testing?
    A It measures the probability that the null hypothesis is true Correct Answer Incorrect Answer
    B It quantifies the probability of observing data at least as extreme as the current sample, assuming the null hypothesis is true Correct Answer Incorrect Answer
    C It determines the strength of the alternative hypothesis Correct Answer Incorrect Answer
    D It represents the probability that the sample mean is accurate Correct Answer Incorrect Answer
    E It defines the critical value for rejecting the null hypothesis Correct Answer Incorrect Answer

    Solution

    The p-value is a key concept in hypothesis testing. It quantifies the probability of obtaining a test statistic that is at least as extreme as the one observed in the sample, assuming the null hypothesis is true. A small p-value (usually less than 0.05) suggests that the observed data is inconsistent with the null hypothesis, leading to the rejection of the null hypothesis in favor of the alternative hypothesis. In contrast, a larger p-value indicates that the observed data is more likely to occur under the null hypothesis, so the null hypothesis is not rejected. Why Other Options Are Wrong : A) Incorrect : The p-value does not provide the probability that the null hypothesis is true. It measures the strength of evidence against the null hypothesis based on the sample data. C) Incorrect : The p-value does not quantify the strength of the alternative hypothesis; it helps assess the evidence against the null hypothesis. D) Incorrect : The p-value is not a measure of the accuracy of the sample mean but is related to the test statistic and the null hypothesis. E) Incorrect : The p-value does not define the critical value for rejecting the null hypothesis. The critical value is determined by the significance level (alpha), whereas the p-value helps  in decision-making based on this threshold.

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