Hypotheses and Conclusions Refer to the hypothesis test described in Exercise 1.

b. If the P-value for the test is reported as “less than 0.001,” what should we conclude about the original claim?

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Identify the null hypothesis (H₀) and the alternative hypothesis (H₁) for the test. The null hypothesis typically represents the default or no-effect assumption, while the alternative hypothesis represents the claim being tested.

Recall the significance level (α) for the hypothesis test. If not explicitly stated, a common default value is α = 0.05.

Compare the reported P-value (less than 0.001) to the significance level (α). If the P-value is less than α, reject the null hypothesis (H₀).

Since the P-value is less than 0.001, it is much smaller than typical significance levels like 0.05 or 0.01. This indicates strong evidence against the null hypothesis (H₀).

Conclude that the original claim, represented by the alternative hypothesis (H₁), is supported by the data. State that there is strong evidence to reject the null hypothesis in favor of the alternative hypothesis.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a default position, and the alternative hypothesis (H1), which represents the claim being tested. The goal is to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative.

P-value

The P-value is a measure that helps determine the strength of the evidence against the null hypothesis. It represents the probability of obtaining results at least as extreme as the observed results, assuming that the null hypothesis is true. A smaller P-value indicates stronger evidence against the null hypothesis, with common thresholds being 0.05, 0.01, and 0.001.

Statistical Significance

Statistical significance refers to the likelihood that a relationship observed in data is not due to random chance. When the P-value is less than a predetermined significance level (often 0.05), the results are considered statistically significant, leading to the rejection of the null hypothesis. In this case, a P-value less than 0.001 suggests very strong evidence against the null hypothesis, indicating that the original claim is likely true.

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