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A researcher is testing a new fertilizer to determine whether it encourages plant growth. One group of oak tree saplings is treated weekly with the new fertilizer, while another group of oak tree saplings is not. Their heights are recorded weekly. After 10 weeks, the results are compared. The researcher finds that the average difference in the heights of the fertilized saplings versus the nonfertilized saplings is 1.5 centimeters. She then generates a simulation of 96 more trials. Examine the histogram of the simulation of differences. Do the data and the simulations provide evidence that the fertilizer has encouraged growth? (1 point) Responses The data and simulations show no evidence that the fertilizer encourages growth. The average height falls in the bin near the center of the distribution, between 0–2, indicating that the difference is not unusual. The data and simulations show no evidence that the fertilizer encourages growth. The average height falls in the bin near the center of the distribution, between 0–2, indicating that the difference is not unusual. The data and simulations show no evidence that the fertilizer encourages growth. The average height falls in the bin near the center of the distribution, between 0–2, indicating that the difference is unusual. The data and simulations show no evidence that the fertilizer encourages growth. The average height falls in the bin near the center of the distribution, between 0–2, indicating that the difference is unusual. The data and simulations show evidence that the fertilizer encourages growth. The average height falls in the bin near the center of the distribution, between 0–2, indicating that the difference is unusual. The data and simulations show evidence that the fertilizer encourages growth. The average height falls in the bin near the center of the distribution, between 0–2, indicating that the difference is unusual. The data and simulations show evidence that the fertilizer encourages growth. The average height falls in the bin near the center of the distribution, between 0–2, indicating that the difference is not unusual.

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To determine whether the fertilizer encourages plant growth, the researcher examines the average difference in heights of treated versus non-treated saplings (1.5 centimeters) and compares it to the distribution of differences from the 96 simulations.

If the average height difference of 1.5 centimeters falls within the region around the center (0–2 cm) of the distribution of simulated differences, it indicates that this finding is not unusual. Generally, for a result to be considered statistically significant, it should be located in the tail of the distribution, meaning it is uncommon under the null hypothesis (which assumes there is no effect of the fertilizer).

Given the response options:

  1. If the average height difference of 1.5 cm falls in the bin near the center (0–2 cm) of the distribution, it suggests that there is no unusual difference in height, and therefore, there is no evidence that the fertilizer encourages growth.

  2. Conversely, if the average height difference falls outside this central area (in the tails), it would indicate an unusual result and could suggest that the fertilizer has a significant effect.

Based on the context you've provided, if the average difference indeed falls in the center bin (0–2 cm), the conclusion to select would be:

"The data and simulations show no evidence that the fertilizer encourages growth. The average height falls in the bin near the center of the distribution, between 0–2, indicating that the difference is not unusual."