To determine the probability of the treatment group's mean being lower than the control group's mean by 15 points or more, we need to know the means and the standard deviation of both groups, as well as the sample size and the correlation between the two groups. Without this information, we cannot calculate the exact probability.
However, we can make a statement about the significance level. If the significance level is set at 5%, this means that the probability of obtaining a result as extreme as or more extreme than the observed result (assuming the null hypothesis is true) is 5% or less. In other words, if the probability of the result is less than 5%, we would reject the null hypothesis and conclude that the treatment group's mean is significantly different from the control group's mean.
So, the completed statement would be:
The significance level is set at 5%, and the probability of the result being as extreme as or more extreme than the observed result is less than 5%, which is lower than the significance level. The result is statistically significant.