A researcher measured the reported distances of two small groups of randomly selected GPS units. They found that the difference in sample means (μ₠âˆ' μ₂) is 0.22 miles. Which conclusion is appropriate from a t-test of the hypothesis Hâ‚€: μ₠= μ₂ versus Ha: μ₠≠ μ₂ if the p-value is 0.025 and the significance level is α = 0.05?
Reject H0 based on evidence that the mean reported distance difference is not 0 miles.
The p-value of 0.025 is less than the significance level of α = 0.05, indicating sufficient evidence to reject the null hypothesis (H0) in favor of the alternative hypothesis (Ha). This suggests that the difference in sample means is statistically significant, providing support for the claim that the means of the two groups are different.
This choice incorrectly interprets the relationship between the sample mean difference and the hypothesis test. The fact that the mean difference is greater than 0 does not justify failing to reject H0; instead, the p-value is what determines whether to reject or fail to reject the null hypothesis.
This choice correctly identifies that the p-value of 0.025 is less than the significance level of 0.05, which provides strong evidence against the null hypothesis. Therefore, we conclude that there is a statistically significant difference in means between the two groups.
This option misrepresents the findings of the t-test. Given the p-value is below the significance level, there is sufficient evidence to reject H0, contrary to the assertion made in this choice that suggests insufficient evidence.
This choice is logically flawed as it contradicts the outcome of the hypothesis test. Rejecting H0 implies that we are claiming the mean difference is not equal to 0 miles, not that it is equal. The evidence supports the difference, not the null hypothesis.
In conclusion, the statistical analysis indicates that with a p-value of 0.025, there is significant evidence to reject the null hypothesis and accept the alternative hypothesis. This demonstrates that the mean distance difference of 0.22 miles is statistically significant, suggesting a real difference between the groups being studied. Understanding the implications of p-values and hypothesis testing is critical in research analysis.
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