Performing a Re-randomization Simulation In this task, you’ll perform a re-randomization simulation to determine whether the difference of the sample means is statistically significant enough to be attributed to the treatment.

Suppose you have 10 green bell peppers of various sizes from plants that have been part of an experimental study. The study involved treating the pepper plants with a nutrient supplement that would produce larger and heavier peppers. To test the supplement, only 5 out of the 10 peppers come from plants that were treated with the supplement. All 10 peppers were of the same variety and grown under similar conditions, other than the treatment applied to 5 of the pepper plants.

Your task is to examine the claim that the nutrient supplement yields larger peppers. You will base your conclusions on the weight data of the peppers. The table shows the weights of the 10 peppers, in ounces. (Note: Do not be concerned with which peppers received the treatment for now.) In this task, you’ll divide the data into two portions several times, take their means, and find the differences of the means. This process will create a set of differences of means that you can analyze to see whether the treatment was successful.

Pepper # 1 2 3 4 5 6 7 8 9 10
Weight (oz) 8.2 9.7 12.1 11.5 13.8 13.6 11.2 14.6 9.2 15.9
Part A
Question
A random number generator assigned each pepper to one of two groups. The weights of the peppers in each group, given three randomizations, appear in the tables.

First Randomization
Group A Group B
13.6 9.2
12.1 8.2
15.9 11.5
11.2 13.8
9.7 14.6
Second Randomization
Group A Group B
8.2 12.1
13.8 14.6
15.9 13.6
9.2 11.2
9.7 11.5
Third Randomization
Group A Group B
8.2 12.1
9.7 13.8
11.5 13.6
14.6 11.2
15.9 9.2
For each table, calculate the mean weight for each group, and , and find the difference of the mean of group A and the mean of group B ().

Type the correct answer in each box.

After the first randomization, is
, is
, and () is
.
After the second randomization, is
, is
, and () is
.
After the third randomization, is
, is
, and () is
.
Part B
Question
What do large differences of the means of each group indicate? Select the correct answer.

The large differences do not indicate any significant meaning in the given context.

The peppers with different weights aren’t properly distributed between the two groups.

There is not enough information to analyze the differences.

The peppers with different weights are properly distributed between the two groups.

Part C
Question
Consider two groups of randomly selected peppers, where neither group has all big or all small peppers.

A mean difference of zero indicates the peppers
well distributed between the two groups.