Henderson determines that a sample size of 138 is required to determine, with 95% confidence (α = 0.05), the maximum proportion of defective 50 mm copper piping in the population. What is the calculated proportion (p̂)?

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TheoryPractice · Accepted Answer

0.10. To calculate the proportion (p̂), we can use the equation n = (Zα/2/E)2 p̂(1 - p̂), where:

α = 0.05
E = 0.05
p̂ = ?
n = 138

Referring to a standard normal distribution table, we find that α/2 (0.025) corresponds to Z = 1.96. Plugging in the values, we can solve for p̂: 138 = ((1.96)/0.05))2 (p̂(1-p̂)). After solving the equation, we find that p̂ = 0.10

Henderson determines that a sample size of 138 is required to determine, with 95% confidence (α = 0.05), the maximum proportion of defective 50 mm copper piping in the population. What is the calculated proportion (p̂)?

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