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A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77 (AAI Journal, February 2006). The survey is con- ducted annually. With the historical data available, assume a known population standard deviation of $15. a. Using the sample data, what is the margin of error associated with a 95% confidence 4. interval? Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share. b.
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Answer #1

a. For 95% confidence interval, Z*-value = 1.96

Margin of safety = Z* x (standard deviation) / sqrt (sample) = 1.96 x (15 / sqrt (100)) = 2.94

b. Confidence interval = (Mean - Margin of error) to (mean + margin of error) = (50 - 2.94) to (50+2.94) = [$47.06, $52.94]

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