A study investigated whether injecting mice with a certain hormone would affect the time it takes them to learn a task. Learning times of 12 mice with the hormone injected were compared with those of 12 mice without the hormone injected. The mean of the learning times for each of the two conditions was calculated. Then, the difference of the means was calculated:
mean(no hormone injected) – mean(hormone injected) = 30 seconds
All 24 measurements were then randomly divided into two groups of 12. This was repeated 400 times, and each time the difference of the group means was calculated. Which outcome of this re-sampling procedure would most strongly support the hypothesis that the hormone improves learning in mice?
A. In 200 cases the difference was greater than or equal to 12.
B. In 24 cases the difference was less than or equal to 12.
C. In 6 cases the absolute value of the difference was greater than or equal to 30.
D. In 12 cases the absolute value of the difference was less than or equal to 30.
I think its B
To determine which outcome of the re-sampling procedure would most strongly support the hypothesis that the hormone improves learning in mice, we need to understand how the re-sampling procedure works.
The re-sampling procedure involves randomly dividing the 24 measurements (from both groups) into two groups of 12. This is repeated 400 times, and each time the difference of the group means is calculated. We are looking for an outcome that supports the hypothesis that the hormone improves learning in mice.
Let's analyze the given answer options:
A. In 200 cases the difference was greater than or equal to 12.
This means that in 200 out of 400 repetitions, the difference between the group means was greater than or equal to 12 seconds. This outcome suggests that the hormone may not have a significant effect on learning since the difference is not consistently in favor of the hormone injected group.
B. In 24 cases the difference was less than or equal to 12.
This means that in 24 out of 400 repetitions, the difference between the group means was less than or equal to 12 seconds. This outcome actually supports the hypothesis that the hormone improves learning in mice. It suggests that the hormone injected group consistently has lower mean learning times compared to the group without the hormone.
C. In 6 cases the absolute value of the difference was greater than or equal to 30.
This means that in 6 out of 400 repetitions, the absolute value of the difference between the group means was greater than or equal to 30 seconds. This outcome suggests that there might be a large effect of the hormone on learning times, but it is not as consistent as option B.
D. In 12 cases the absolute value of the difference was less than or equal to 30.
This means that in 12 out of 400 repetitions, the absolute value of the difference between the group means was less than or equal to 30 seconds. This outcome suggests that the hormone may not have a significant effect on learning since the difference is not consistently in favor of the hormone injected group.
Given the options, B is the most suitable outcome that supports the hypothesis that the hormone improves learning in mice.
The correct answer is C. In 6 cases the absolute value of the difference was greater than or equal to 30.
In this re-sampling procedure, the researchers are comparing the difference in means between the two groups (hormone injected and no hormone injected) in order to determine if the hormone improves learning in mice. By randomly dividing the measurements into groups multiple times and calculating the difference of the means each time, they are creating a distribution of possible differences.
If the hormone does not actually improve learning, then the distribution of differences of means should be centered around zero. However, if the hormone does improve learning, we would expect the distribution to have a positive mean, indicating that the difference in means is consistently larger when comparing the hormone injected group to the no hormone injected group.
Therefore, the outcome that most strongly supports the hypothesis that the hormone improves learning in mice is option C, where in 6 cases the absolute value of the difference was greater than or equal to 30. This suggests that the difference in means between the two groups is consistently larger than 30 seconds, indicating a potential improvement in learning with the hormone.