Question

    In hypothesis testing, what does a low p-value (e.g., p

    < 0.05) suggest about the null hypothesis?
    A The null hypothesis is accepted. Correct Answer Incorrect Answer
    B There is no evidence to support the alternative hypothesis. Correct Answer Incorrect Answer
    C The null hypothesis can be rejected with high confidence. Correct Answer Incorrect Answer
    D The sample size is too small to conclude. Correct Answer Incorrect Answer
    E The results are likely due to sampling error. Correct Answer Incorrect Answer

    Solution

    A low p-value, typically below 0.05, suggests that the observed data is unlikely to occur if the null hypothesis were true. This provides strong evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating that there is a statistically significant effect or relationship present in the data. The threshold of 0.05 reflects a 5% risk of committing a Type I error (false positive), which is generally acceptable in many fields of research, making the result statistically reliable and meaningful. The other options are incorrect because: • Option 1 is incorrect; a low p-value provides evidence against, not for, the null hypothesis. • Option 2 misinterprets the p-value’s role, as a low p-value supports the alternative hypothesis. • Option 4 relates to power analysis, not directly to p-value interpretation. • Option 5 is incorrect; a low p-value suggests statistical significance, not sampling error.

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