A study of students taking Statistics 101 was done. Four hundred students who studied for more than 10 hours averaged a B. Two hundred students who studied for less than 10 hours averaged a C. This difference was significant at the 0.01 level. What does this mean?
There is less than a 0.01 chance that the first group’s grades were better by chance alone.
In statistics, hypothesis testing is used to determine whether the observed difference between two groups is statistically significant. The significance level, often denoted as α (alpha), is a predetermined threshold to determine the level of evidence required to reject the null hypothesis.
Here, the study compares two groups of students: those who studied for more than 10 hours (400 students) and those who studied for less than 10 hours (200 students). The average grade of those who studied for more than 10 hours was a B, while the average grade of those who studied for less than 10 hours was a C.
The statement "This difference was significant at the 0.01 level" means that the observed difference in the averages between the two groups is unlikely to have occurred due to random chance alone.
More specifically, a significance level of 0.01 means that there is a 1% probability of observing such a significant difference in the average grades between the two groups, assuming that the null hypothesis (no difference between the groups) is true.
Since the observed difference was deemed statistically significant at the 0.01 significance level, it suggests that there is strong evidence to reject the null hypothesis and conclude that the difference in grades between the two groups is unlikely to be due to chance.