True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.


A large P-value in a test will favor rejection of the null hypothesis.

Verified step by step guidance

1. Understand the concept of a P-value: The P-value in hypothesis testing measures the probability of observing a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true.
2. Recall the decision rule for hypothesis testing: A small P-value (typically less than the significance level, α, such as 0.05) provides evidence to reject the null hypothesis. Conversely, a large P-value suggests insufficient evidence to reject the null hypothesis.
3. Analyze the statement: The statement claims that a large P-value favors rejection of the null hypothesis. This contradicts the decision rule, as a large P-value indicates that the null hypothesis is likely true or that there is insufficient evidence to reject it.
4. Rewrite the statement as true: A correct version of the statement would be, 'A large P-value in a test suggests insufficient evidence to reject the null hypothesis.'
5. Conclude: The original statement is false, and the corrected version clarifies the relationship between P-values and hypothesis testing decisions.

Key Concepts

P-value

The P-value is a statistical measure that helps determine the significance of results in hypothesis testing. It represents the probability of obtaining results at least as extreme as the observed results, assuming the null hypothesis is true. A smaller P-value indicates stronger evidence against the null hypothesis, while a larger P-value suggests weaker evidence.

Null Hypothesis

The null hypothesis is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing. Researchers aim to test this hypothesis against an alternative hypothesis, which posits that there is an effect or a difference. The outcome of the test will either lead to the rejection or failure to reject the null hypothesis based on the evidence provided by the data.

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about population parameters based on sample data. It involves formulating a null hypothesis and an alternative hypothesis, calculating a test statistic, and determining the P-value to assess the strength of evidence against the null hypothesis. The decision to reject or not reject the null hypothesis is made based on the P-value in relation to a predetermined significance level.