In a sample of 2.000 items taken from a large lot. 80 are found to be nonconforming. What is the 95% confidence interval for the proportion of nonconforming items?
To calculate the 95% confidence interval for the proportion of nonconforming items in a sample, we use the formula for the confidence interval for a proportion: p̂ ± Z * √(p̂(1-p̂)/n), where p̂ is the sample proportion (80/2000 = 0.04), Z is the Z-score for a 95% confidence level (1.96), and n is the sample size (2000). Plugging in the values, we get the confidence interval as [0.0308, 0.0499]. Reference: "Statistics for Engineers and Scientists" by William Navidi, which explains confidence intervals and their calculations.
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