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To determine the minimum sample size required to confirm the significance of a shift in the mean output, you need to consider the statistical power of the test, the population standard deviation, the expected shift in the mean (in this case, more than 12,000 pounds), and the desired confidence level (95%). Considering the factors involved, an adequate sample size must ensure that the findings are statistically reliable. A sample size of 35 is generally a sufficient amount in quality control settings to capture the variability in the data and accurately reflect the true mean. It provides enough statistical power to detect a shift in the mean output and validate its significance at the specified confidence level. Adequate sample size helps mitigate the risk of Type I and Type II errors, ensuring the conclusions drawn are robust and valid. In contrast, smaller sample sizes, such as 5 or 3, would likely lack the power to detect a meaningful shift of more than 12,000 pounds with confidence. A sample size of 21, while larger than the minimum, may not provide enough assurance to confidently assert the shift in the mean's significance compared to a higher sample size like 35, which offers a better balance between practical considerations and statistical rigor.