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    Question

    In hypothesis testing, a p-value of 0.03 indicates

    that:
    A There is a 3% chance that the null hypothesis is true. Correct Answer Incorrect Answer
    B The observed data is 3% likely to occur if the null hypothesis is true. Correct Answer Incorrect Answer
    C The null hypothesis can be rejected with 97% confidence. Correct Answer Incorrect Answer
    D The observed data is highly significant and the null hypothesis is proven false. Correct Answer Incorrect Answer
    E The test does not provide enough evidence to reject the null hypothesis. Correct Answer Incorrect Answer

    Solution

    In hypothesis testing, the p-value represents the probability of observing the data (or something more extreme) assuming the null hypothesis is true. A p-value of 0.03 means that there is a 3% probability that the observed data (or more extreme results) could occur if the null hypothesis is actually true. If the p-value is below a predetermined significance level (e.g., 0.05), the null hypothesis is typically rejected, suggesting that the results are statistically significant. However, the p-value does not indicate the probability that the null hypothesis is true or false; it only measures the likelihood of obtaining the observed data under the assumption of the null hypothesis. Why Other Options Are Incorrect: • A: The p-value does not directly indicate the probability that the null hypothesis is true. • C: The p-value does not measure confidence; it measures the probability of observing the data given the null hypothesis. • D: A p-value of 0.03 suggests statistical significance but does not "prove" the null hypothesis false. It indicates evidence against the null hypothesis. • E: A p-value of 0.03 suggests that the null hypothesis can be rejected at a 5% significance level, so there is enough evidence to reject the null hypothesis.

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