Preventing the Spread of Foot and Mouth Disease in Pig Farms
Is the sample size big enough to be cost-effective in testing pigs for Foot and Mouth Disease?
During the outbreaks, 7 pigs were found to be positive in an area with 2000 pigs. There are a further 10 000 pigs in 8 other areas adjoining the infected area. We have sufficient funds to test 1000 pigs and the confidence required is 99% that no pig in the sample will be found to be positive. Is this sample big enough to be cost-effective?
Answer:
To determine if the sample size is cost-effective, we can calculate the required sample size using a formula called the Sample Size Calculation. By substituting the values into the formula, we can determine that the sample size of 1000 pigs is larger than the required sample size, making it cost-effective.
Explanation: To determine if the sample size is big enough to be cost-effective, we can use a formula called the Sample Size Calculation. The formula is: n = ((Z-score)² * p * (1-p))/(E²) Where: n is the required sample size Z-score is the number of standard deviations corresponding to the desired confidence level (in this case, 99%) p is the estimated proportion of pigs that would test positive for Foot and Mouth Disease E is the desired margin of error (precision) In this case, we know that 7 out of 2000 pigs tested positive. Therefore, the estimated proportion (p) is 7/2000 = 0.0035. Given that we want a confidence level of 99%, the Z-score corresponding to this confidence level is approximately 2.576. By substituting the values into the formula, we can calculate the required sample size: n = ((2.576)² * 0.0035 * (1-0.0035))/(0.002) n ≈ 190.172 Therefore, the sample size of 1000 pigs is larger than the required sample size of 190.172, making it cost-effective to conduct this sample.