Gardeners often use either chemicals or fences to protect their plants from pests. 60 gardeners were asked about their plant protection method and its success. Three of the 13 who used chemicals had pests. Seven of the 47 who used fences had pests.

Please answer both questions.

i) What percent of gardeners overall had pests?

ii) Which protection method was more effective?

Question

Gardeners often use either chemicals or fences to protect their plants from pests. 60 gardeners were asked about their plant protection method and its success. Three of the 13 who used chemicals had pests. Seven of the 47 who used fences had pests.

Please answer both questions.

i) What percent of gardeners overall had pests?

ii) Which protection method was more effective?

BlackTom AI · Accepted Answer

First, lay out what the problem states and what needs to be found. We have 60 gardeners total: 13 used chemicals (with 3 having pests) and 47 used fences (with 7 having pests). We need (i) the overall percent of gardeners who had pests, and (ii) which method was more effective.

Step for (i): determine the total number of gardeners who had pests. Among chemical users: 3 had pests. Among fence users: 7 had pests. Total with pests = 3 + 7 = 10.

Step for (i): compute the overall percentage of pests among all gardeners. Total gardeners = 60. Percentage with pests = (10 / 60) × 100 = 16.666…%, which rounds to 16.67%.

Step for (ii): compare the effectiveness of the two methods by looking at the pest rate within each group.
- Chemicals: 3 pests out of 13 users → 3/13 ≈ 23.08% pest rate.
- Fences: 7 pests out of 47 users → 7/47 ≈ 14.89% pest rate.

Interpretation: a smaller pest rate indicates better protection. Since fences have a lower pest rate (≈14.89% vs. ≈23.08% for chemicals), the fence method was more effective at protecting plants.

Additional notes: the overall pest rate (16.67%) combines both groups, but it doesn’t reflect the differing effectiveness by method. When evaluating protection strategies, the direct comparison of pest rates within each method provides clearer insight into relative effectiveness.

In summary, the overall pest percentage is 16.67%, and fences were more effective at preventing pests than chemicals because the pest rate among fence users is lower than that among chemical users.

STAT 1450.02 SP2025 (28132) Checkpoint 13.7

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