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 consider the information provided and evaluate the options.

In the study, two groups of mice were compared: one group with the hormone injected and another group without the hormone. The mean of the learning times for each group was calculated, and the difference of the means was found to be 30 seconds.

During the re-sampling procedure, the 24 measurements were randomly divided into two groups of 12, and this process was repeated 400 times. Each time, the difference of the group means was calculated.

Now, let's evaluate the options:

A. In 200 cases, the difference was greater than or equal to 12.
This option doesn't provide strong support for the hypothesis since it only states that the difference is greater than or equal to 12. It doesn't take into account the original difference observed (30 seconds).

B. In 24 cases, the difference was less than or equal to 12.
This option doesn't provide strong support for the hypothesis either since it only considers cases where the difference is less than or equal to 12. It also doesn't take into account the original difference observed (30 seconds).

C. In 6 cases, the absolute value of the difference was greater than or equal to 30.
This option provides stronger support for the hypothesis. Since the original difference observed was 30 seconds, if in 6 cases the absolute value of the difference was greater than or equal to 30, it suggests that the hormone may have a significant effect on learning times.

D. In 12 cases, the absolute value of the difference was less than or equal to 30.
This option doesn't provide strong support for the hypothesis since it only considers cases where the absolute value of the difference is less than or equal to 30. It doesn't take into account the original difference observed (30 seconds).

Based on the above analysis, the option that would most strongly support the hypothesis that the hormone improves learning in mice is C. In 6 cases, the absolute value of the difference was greater than or equal to 30.