Question

1. There are 25 students who started computer programming in elementary school and 25 students who started computer programming in middle school. The first group had a mean final project grade of 95% and the second group had a mean final project grade of 92%.

The line plot shows the differences after 10 rerandomizations. Determine whether the difference in the means of the two groups is significant based on the line plot. Explain your answer.

Answer 1

the difference in the means is not significant

Explanation:

Let’s begin first by finding the difference between the means of the 2 groups.

Difference in means = 95% - 92% = 3% Now let’s look at the line plot of the 10 rerandomizations. On that plot, 4 of the randomizations have a difference of 3.

Probability of having a difference of 3 = 4 / 10 *100% = 40%

So just by mixing up the scores from both classes and finding the difference between the mean of 2 randomly defined groups, there was a difference of 3 between the 2 means in 40% of the trials.

Since this probability is so large, the difference in the means is not significant. The line plot shows that it would be very likely that the difference in the means is just due to random chance

Answer 2

the answer is attached below