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

Suppose you have 10 green bell peppers of various sizes that have been part of an experimental study. The study involved treating the peppers with a nutrient supplement that would produce larger and heavier peppers. To test the supplement, only 5 out of 10 peppers 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 peppers.

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 right 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 will create a set of differences of means that you can analyze to see if 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
Type the correct answer in each box.

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 ().

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
What does the difference of the means of each group indicate? What makes the mean of one group greater or less than the mean of the other group?

Font Sizes

Characters used: 0 / 15000
Part C
What does a mean difference of zero between the two groups indicate?

Font Sizes