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 the process and compare the outcome with the original difference in means (30 seconds).
In the study, the researchers calculated the mean learning times for both groups (hormone injected and no hormone injected). They then subtracted the mean of the hormone-injected group from the mean of the no hormone injected group to get a difference of means of 30 seconds.
In the re-sampling procedure, all 24 measurements were randomly divided into two groups of 12. This process was repeated 400 times, and each time the difference of the group means was calculated.
Now, let's analyze the given outcomes:
A. In 200 cases, the difference was greater than or equal to 12.
This outcome suggests that in 200 out of 400 re-samplings, the difference in means was greater than or equal to 12 seconds. However, since the original difference in means was 30 seconds, this outcome is less supportive of the hypothesis that the hormone improves learning.
B. In 24 cases, the difference was less than or equal to 12.
This outcome suggests that in 24 out of 400 re-samplings, the difference in means was less than or equal to 12 seconds. Since the original difference in means was 30 seconds, this outcome is not supportive of the hypothesis that the hormone improves learning.
C. In 6 cases, the absolute value of the difference was greater than or equal to 30.
This outcome suggests that in 6 out of 400 re-samplings, the absolute value of the difference in means was greater than or equal to 30 seconds. Since the original difference in means was 30 seconds, this outcome provides some support for the hypothesis that the hormone improves learning in mice.
D. In 12 cases, the absolute value of the difference was less than or equal to 30.
This outcome suggests that in 12 out of 400 re-samplings, the absolute value of the difference in means was less than or equal to 30 seconds. Since the original difference in means was 30 seconds, this outcome is not supportive of the hypothesis that the hormone improves learning.
Based on the analysis, the outcome that most strongly supports the hypothesis that the hormone improves learning in mice would be option C, where in 6 cases the absolute value of the difference was greater than or equal to 30.