A pedagogical research institute wanted to test whether a new method for teaching geometry helps students achieve better scores. At the beginning of the semester, $800$ students were randomized between a treatment group and a control group. The treatment group was taught using the new method, and the control group was taught using traditional methods. By the end of the semester, the researchers compared the participants’ scores in the Geometry section of the final exam. The results of the experiment showed that the mean score of the treatment group is $8$ points greater than the mean score of the control group. To test whether the results could be explained by random chance, the researchers created the table below, which summarizes the results of $1000$ re-randomizations of the data (with differences between means rounded to the nearest $2$ points). **According to the simulations, what is the probability of the treatment group's mean being higher than the control group's mean by $8$ points or more?** $\qquad$[[☃ input-number 1]] Assume that if the probability you found is *lower* than $5\%$, then the result should be considered significant. **What should we conclude regarding the experiment's result?** [[☃ radio 1]] Treatment group mean $-$ Control group mean | Frequency :-: | :-: $-14$ | $2$ $-12$ | $7$ $-10$ | $26$ $-8$ | $43$ $-6$ | $91$ $-4$ | $107$ $-2$ | $131$ $0$ | $177$ $2$ | $144$ $4$ | $110$ $6$ | $73$ $8$ | $52$ $10$ | $27$ $12$ | $8$ $14$ | $2$