Question

The reaction times are measured for 50 college students who are randomly assigned to two groups. The students in group 1 listen to loud music during the test and the students in group 2 perform the test in silence. There are 25 students in each group. The mean for the loud-music group is 2.64 seconds, and the mean for the silent

group is 3.22 seconds. The data for both groups is combined, 25 reaction times are selected at random, and the mean of these reaction times is compared to the mean
of the remaining 25 reaction times. This process is repeated 14 times. The means for
the groups are summarized in the table.
Is the difference in the mean reaction times from the original experimental groups likely due to chance, or is the evidence that the music has an effect on reaction time? Explain your reasoning.

Answer 1

See below.

Explanation:

In this analysis, the key question is whether the observed mean difference between the loud music and silence groups is unusual compared to what we'd expect if there were no real difference between the groups (i.e., due to random chance alone). The p-value tells us the likelihood of observing such a mean difference under the null hypothesis.

If the p-value is small, it suggests that the difference in reaction times is unlikely to have occurred by chance alone, providing evidence that music has an effect on reaction time. Conversely, if the p-value is large, it suggests that the observed difference could have occurred due to random sampling variability, and there is no strong evidence for an effect of music on reaction time.