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?
Reject H0 based on evidence that the mean reported distance difference is less than 0 miles.
The p-value of 0.012 is less than the significance level of 0.05, which indicates strong evidence against the null hypothesis (H0). Therefore, we reject H0 and conclude that the mean reported distance of group one is significantly less than that of group two.
This choice is incorrect because the reported mean difference is -0.24 miles, which indicates that the mean for group one is less than for group two. Rejecting H0 based on a difference being greater than 0 is not supported by the data.
This choice is incorrect since the p-value of 0.012 provides sufficient evidence to reject the null hypothesis. The evidence clearly indicates that the mean difference is statistically significant and supports the assertion that group one's mean is less than group two's.
While it is true that the mean difference is -0.24 miles, this choice misinterprets the implications of the p-value. Since the p-value is below the significance threshold, we actually have enough evidence to reject H0, rather than failing to reject it.
This choice is correct, as it accurately reflects the result of the t-test. Given that the p-value is 0.012, which is less than the alpha level of 0.05, we reject H0 and conclude that the mean reported distance for group one is significantly less than that for group two.
In hypothesis testing, the p-value serves as a critical tool for decision-making regarding the null hypothesis. In this scenario, the p-value indicates strong evidence that the mean difference is indeed less than 0 miles, leading to the rejection of H0. Thus, the conclusion supports the alternative hypothesis, affirming a significant difference in means between the two groups.
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