Question

Each month a lawn-care company sprays for weeds in 500 different yards. Last month, to determine the effectiveness of its herbicide, the company randomly selected 50 lawns for inspection. Of the lawns selected, 40 showed 5 or fewer weeds. Which of the following could the lawn company conclude with the greatest certainty?

a) The herbicide is ineffective.
b) The herbicide is highly effective.
c) The herbicide has variable effectiveness.
d) The herbicide's effectiveness is unknown.

Answer 1

Based on the data of 40 out of 50 lawns showing 5 or fewer weeds, the company could most certainly conclude that the herbicide has variable effectiveness. Complete effectiveness cannot be established as some weeds were still present, and the inspection only covered a sample of all treated lawns.

Step-by-step explanation:

The question concerns the effectiveness of a herbicide used by a lawn-care company. To answer this, they monitored 50 of the 500 lawns and found that 40 had 5 or fewer weeds. Considering the available options, with 80% of the inspected lawns showing positive results, the lawn company could conclude with greatest certainty that c) the herbicide has variable effectiveness.

This is because while the results are generally positive, we do not know how the other 450 lawns fared, and if the 50 lawns inspected are truly representative of the entire population. Additionally, since some weeds were still present, the herbicide was not completely effective. This real-world effectiveness may be influenced by many factors such as application method, environmental conditions, or the presence of resistant weeds.