A study of two types of weed killers was done on two identical weed plots. One weed killer killed 15% more weeds than the other. This difference was significant at the 0.05 level. What does this mean?
A. The improvement was due to the fact that there were more weeds in one study.
B. The probability that the difference was due to chance alone is greater than 0.05.
C. The probability that one weed killer performed better by chance alone is less than 0.05.
D. There is not enough information to make any conclusion.
To answer this question, we need to understand what a significance level is and what it means in the context of a study.
In statistics, a significance level, denoted as α, is the threshold at which we determine whether a result is statistically significant or not. It represents the probability of observing a difference as extreme or more extreme than the one observed, purely due to chance.
In this case, the fact that the difference between the two types of weed killers was found to be significant at the 0.05 (or 5%) level means that the probability that the observed difference was due to chance alone is less than 0.05.
Therefore, the correct answer is C. The probability that one weed killer performed better by chance alone is less than 0.05.
This suggests that there is evidence to support the conclusion that one weed killer is more effective than the other, and the difference in weed-killing performance is not likely to be a random occurrence.
Option A suggests that the improvement is due to there being more weeds in one study, but the question states that the weed plots were identical, so this is not a plausible explanation.
Option B states that the probability that the difference was due to chance alone is greater than 0.05, which is the opposite of what the significance level implies.
Option D suggests that there is not enough information to make any conclusion, but we have enough information to determine that there is a significance difference between the two weed killers.