22. 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?
Answer: A
Fail to reject H0 because there is insufficient evidence that the mean yield difference is greater than 0 bushels per acre.
Given the p-value of 0.177, which is greater than the significance level of 0.02, there is insufficient evidence to reject the null hypothesis. This indicates that the observed difference in mean yields does not provide strong enough evidence to conclude that the mean yield difference is greater than zero.
A) Fail to reject H0 because there is insufficient evidence that the mean yield difference is greater than 0 bushels per acre.
This option is correct because the p-value of 0.177 exceeds the significance level of 0.02, indicating that the data does not provide enough evidence to support the alternative hypothesis that the mean yield difference is greater than zero. Thus, we fail to reject the null hypothesis.
B) Fail to reject H0 based on the fact that the mean difference of 1.81 bushels per acre is greater than 0 bushels per acre.
This option is incorrect because simply having a positive mean difference does not justify failing to reject the null hypothesis. The decision to reject or not reject H0 is based on the p-value in relation to the significance level, not solely on the value of the mean difference.
C) Reject H0 based on evidence that the mean yield difference is greater than 0 bushels per acre.
This option is incorrect as it contradicts the findings from the t-test. The p-value of 0.177 indicates that we do not have sufficient evidence to reject the null hypothesis, meaning we cannot conclude that the mean yield difference is significantly greater than zero.
D) Reject H0 based on evidence that the mean yield difference is less than 0 bushels per acre.
This option is incorrect because the mean yield difference is actually 1.81 bushels per acre, which is greater than zero. Additionally, the rejection of H0 is not supported by the p-value, which does not indicate significant evidence for rejecting H0 in favor of the alternative hypothesis.
Conclusion
The correct answer is A, as the p-value of 0.177 indicates that there is insufficient evidence to reject the null hypothesis at the 0.02 significance level. Options B, C, and D fail to recognize the importance of the p-value in hypothesis testing, leading to incorrect conclusions about the significance of the mean yield difference.