Travis is testing the effects of a new fertilizer on the growth of a plant. He had 30 plants that were randomly split into two groups. Group 1 was given no fertilizer, and in Group 2 each plant was given a cup of fertilizer. Two weeks later, the height of each plant was measured. Travis found that the mean of the heights from Group 2 was 1.5 inches taller than the mean of the heights from Group 1.
To confirm that the fertilizer was the cause of the difference, Travis re-randomized the data into two groups 300 times and looked at the resulting differences in the means. The difference in the means was greater than or equal to 1.5 inches 2 times out of the 300 trials.
What do the results of the re-randomization mean in confirming Travis' test on the effect of the fertilizer? (I chose B, but I'm not sure)
A. They allow Travis to conclude confidently that the fertilizer caused the difference in the mean heights of the plants.
B. They allow Travis to conclude confidently that the fertilizer did not cause the difference in the mean heights of the plants.
C. There is no information gained from the re-randomization on the effect of the fertilizer.
The results of the re-randomization indicate that the fertilizer did not cause the difference in the mean heights of the plants.
To understand why, we need to look at the process of re-randomization and its purpose. In this experiment, Travis re-randomized the data 300 times, meaning he randomly assigned the plants to the two groups 300 times and calculated the differences in the means each time.
If the fertilizer truly had an effect on the plant growth, we would expect to see a significant difference in the means between the two groups in most of the re-randomizations. However, in this case, the difference in the means was greater than or equal to 1.5 inches only 2 out of 300 times. This suggests that the observed 1.5 inch difference in the mean heights between the two groups may have been due to random chance rather than the effect of the fertilizer.
Therefore, the results of the re-randomization indicate that Travis cannot conclude confidently that the fertilizer caused the difference in the mean heights of the plants. This aligns with answer choice B: "They allow Travis to conclude confidently that the fertilizer did not cause the difference in the mean heights of the plants."