14. 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 âˆ'0.24 miles. What is the appropriate conclusion from a t-test of the hypothesis Hâ‚€: μ₠= μ₂ versus Ha: μ₠< μ₂ if the p-value is 0.012 and the significance level is α = 0.05?
Answer: D
Reject H0 based on evidence that the mean reported distance difference is less than 0 miles.
The analysis indicates a statistically significant result with a p-value of 0.012, which is less than the significance level of 0.05. This suggests that there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating that the mean reported distance difference is indeed less than 0 miles.
A) Reject H0 based on evidence that the mean reported distance difference is greater than 0 miles.
This option is incorrect because the difference in sample means is -0.24 miles, which indicates that the mean reported distance for the first group is less than that of the second group. The evidence supports a conclusion that suggests a mean difference less than 0, not greater.
B) Fail to reject H0 because there is insufficient evidence that the mean reported distance difference is less than 0 miles.
This choice is incorrect as the p-value of 0.012 provides strong evidence against the null hypothesis. Since this p-value is below the significance level of 0.05, it indicates sufficient evidence to suggest that the mean reported distance difference is indeed less than 0 miles.
C) Fail to reject H0 based on the fact that the mean difference of -0.24 miles is less than 0 miles.
This option is misleading. While it correctly notes that the mean difference is -0.24 miles, it incorrectly concludes to fail to reject H0. The presence of a significant p-value indicates that we should reject the null hypothesis, not fail to do so.
D) Reject H0 based on evidence that the mean reported distance difference is less than 0 miles.
This is the correct answer as it aligns with the statistical evidence provided. The p-value of 0.012 is less than the significance level of 0.05, supporting the conclusion that the mean difference is significantly less than 0 miles.
Conclusion
The correct decision is to reject H0, as the evidence from the t-test shows a significant p-value indicating that the mean difference is less than 0 miles. All other options incorrectly interpret the results or fail to recognize the implications of the statistical significance, confirming that D is the only valid conclusion based on the given data.