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Question

A histogram has an x-axis labeled Difference in Height left parenthesis count right parenthesis ranging from negative 8 to 8 in increments of 2. The y-axis labeled as Frequency ranging from 0 to 40 in increments of 10.

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 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 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 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.

Answer 1

To determine whether the evidence from the data and simulations suggests that the fertilizer encourages growth, we need to assess where the average difference of 1.5 centimeters falls within the distribution of simulated differences represented in the histogram.

1. The average difference of 1.5 cm is between 0–2 cm based on the information provided.
2. If this average difference falls near the center of the distribution, it indicates that it is a common outcome (not unusual).
3. If the simulation trials show that differences around 1.5 cm are frequent (meaning many trials fall within that region), this would suggest that the fertilizer does not significantly impact growth.

With the information given, an appropriate response could 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 cm, indicating that the difference is not unusual."

So the correct option would be the one stating that the difference is not unusual.