Question 1 Using Alpha 05: What Is Your Decision If The P Va

Question 1using Alpha 05 What Is Your Decision If The P Value Is 0

Using alpha = .05, the decision when the p-value is 0.04 for a one-tailed test is to reject the null hypothesis. Since the p-value (0.04) is less than the significance level (0.05), there is sufficient evidence to reject the null hypothesis, indicating that the observed effect is statistically significant.

Conversely, if the p-value had been greater than 0.05, we would fail to reject the null hypothesis, implying insufficient evidence to confirm a significant effect.

Paper For Above instruction

The interpretation of p-values in hypothesis testing is fundamental to making informed decisions about the validity of research hypotheses. A p-value represents the probability of obtaining an observed effect, or one more extreme, assuming that the null hypothesis is true. When utilizing a significance level (α), such as 0.05, researchers compare the p-value to this threshold to guide their decision-making process.

In the context of a one-tailed test with α = 0.05, if the p-value is less than or equal to 0.05, the null hypothesis is rejected. This outcome suggests that the observed data are unlikely under the null hypothesis, providing evidence in favor of the alternative hypothesis. Specifically, a p-value of 0.04 indicates a 4% probability that the observed data or more extreme results would occur if the null hypothesis were true, which falls below the 5% cutoff, justifying rejection.

It is important to comprehend that the p-value does not measure the probability that the null hypothesis is true; instead, it assesses data compatibility with the null hypothesis. Additionally, the choice of a one-tailed or two-tailed test influences the interpretation of the p-value, with one-tailed tests focusing on effects in a specific direction.

In practice, the decision rule is straightforward: reject H0 if p-value ≤ α, otherwise, do not reject H0. In this case, with p-value = 0.04 and α = 0.05, the decision is to reject the null hypothesis, supporting the claim that the effect or difference under investigation is statistically significant.

Understanding and correctly applying the p-value in hypothesis testing ensures that research conclusions are based on rigorous statistical evidence, minimizing errors and enhancing the reliability of findings.

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