A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He subdivides his six lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half. The following table shows the results. Using 5% significance level, which of the following is an appropriate conclusion that supports or does not support the farmer's claim? A) Reject H₀: µ_D = 0 and therefore conclude that the crop yield with the new fertilizer is not significantly different from the crop yield with the old fertilizer. B) Reject H₀: µ_D = 0 and therefore do not conclude that the crop yield with the new fertilizer is not significantly different from the crop yield with the old fertilizer. C) Do not reject H₀: µ_D = 0 and therefore conclude that the crop yield with the new fertilizer is not significantly different from the crop yield with the old fertilizer. D) Do not reject H₀: µ_D = 0 and therefore do not conclude that the crop yield with the new fertilizer is not significantly different from the crop yield with the old fertilizer.

Question

Quizplus · Accepted Answer

The appropriate hypothesis to test in this case is H₀: µ_D = 0, which states that there is no significant difference in the crop yield with the new fertilizer and the old fertilizer. The test statistic for this hypothesis is a paired t-test, which compares the means of two related samples. Using a 5% significance level, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to say that there is a significant difference in the crop yield. In this case, the p-value is 0.150, which is greater than 0.05, so we do not reject the null hypothesis and conclude that the crop yield with the new fertilizer is not significantly different from the crop yield with the old fertilizer. Therefore, the correct choice is C.

A Farmer Is Concerned That a Change in Fertilizer to an Organic