A researcher measured the agricultural yields of two small groups of randomly selected fields. They found that the difference in sample means (?1 - ?2) is 1.81 bushels per acre. Which conclusion is appropriate from a t-test of the hypothesis H0: ?1 = ?2 versus Ha: ?1 > ?2 if the p-value is 0.177 and the significance level is ? = 0.02?
Fail to reject H0 because there is insufficient evidence that the mean yield difference is greater than 0 bushels per acre.
The p-value of 0.177 is greater than the significance level of 0.02, indicating that there is insufficient statistical evidence to reject the null hypothesis (H0). This suggests that we cannot conclude that the mean agricultural yield difference is greater than zero.
This choice correctly reflects the outcome of the t-test. Since the p-value (0.177) exceeds the significance level (0.02), we do not have enough evidence to support the claim that the mean difference in yields is significantly greater than zero.
This choice misinterprets the significance of the mean difference. While the mean difference is indeed 1.81 bushels per acre, the decision to reject or fail to reject H0 depends on the p-value relative to the significance level, not merely on the size of the mean difference itself.
This choice is incorrect because the p-value (0.177) does not provide sufficient evidence to reject H0. A rejection would require a p-value less than the significance level (0.02), which is not the case here.
This choice is also incorrect. The mean yield difference of 1.81 bushels per acre is positive; thus, there is no basis for concluding that it is less than zero. Furthermore, the decision to reject H0 requires a p-value below the significance level, which is not satisfied.
In hypothesis testing, the p-value serves as a critical threshold for decision-making. Since the p-value of 0.177 exceeds the significance level of 0.02, we fail to reject the null hypothesis, concluding that there is insufficient evidence to assert that the mean yield difference is greater than zero. This emphasizes the importance of not solely relying on observed differences but also considering the statistical significance of the findings.
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