Question

2. A new pesticide company took a random sample of 200 farms using their new product. The results showed that 160 farms no longer have a problem with caterpillars feeding on their crops, with a margin of error of ±13 farms. If the pesticide company is working with 1,470 farms, how many farms will be expected to no longer have a problem with caterpillars feeding on their crops? ​

Answer 1

Answer: To estimate the number of farms expected to no longer have a problem with caterpillars feeding on their crops among the total 1,470 farms based on the random sample of 200 farms, we can use proportion estimation.

First, let's find the proportion of farms in the sample that no longer have a problem with caterpillars:

Proportion = (Number of farms with no caterpillar problem in the sample) / (Total number of farms in the sample)

Proportion = 160 / 200

Proportion = 0.8

Next, we'll use this proportion to estimate the number of farms in the total population of 1,470 farms:

Estimated number of farms = Proportion * Total number of farms in the population

Estimated number of farms = 0.8 * 1,470

Estimated number of farms = 1,176

Therefore, it is expected that approximately 1,176 farms will no longer have a problem with caterpillars feeding on their crops based on the sample data.

Explanation: