Asked by cool boy
In a cafe, the owner surveyed 200 customers about their favorite drink; 42 customers said that they prefer caramel macchiato. Estimate the population proportion using two standard errors. Round answers to two decimal places.(1 point)
≤p≤
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GPT-5 mini
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Sample proportion p̂ = 42/200 = 0.21.
SE = sqrt[p̂(1−p̂)/n] = sqrt(0.21·0.79/200) ≈ 0.03, so 2·SE ≈ 0.0576.
0.21 − 0.0576 = 0.1524 ≈ 0.15
0.21 + 0.0576 = 0.2676 ≈ 0.27
Answer: 0.15 ≤ p ≤ 0.27.
SE = sqrt[p̂(1−p̂)/n] = sqrt(0.21·0.79/200) ≈ 0.03, so 2·SE ≈ 0.0576.
0.21 − 0.0576 = 0.1524 ≈ 0.15
0.21 + 0.0576 = 0.2676 ≈ 0.27
Answer: 0.15 ≤ p ≤ 0.27.
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