A sample survey of 54 discount brokers showed that the
- a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
- b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.
a.
Find the margin of error for 95% confidence interval.
Answer to Problem 48SE
The margin of error for 95% confidence interval is 4.
Explanation of Solution
Calculation:
The given information is that the mean price charge for a trade of 100 shares at $0 per share by a sample of 54 brokers was $33.77 and the population standard deviation is $15.
The formula for margin of error is zα2σ√n.
From the “Table 8.1 value of zα2”, the value of zα2 for 95% is 1.96.
The value of margin of error is
zα2σ√n=1.9615√54=1.96×2.04=4
Thus, the value of margin of error is 4.
b.
Find the 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share.
Answer to Problem 48SE
The 95% confidence interval for mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77, $37.77).
Explanation of Solution
Calculation:
From Part (a), the margin of error is 4.
The mean value for the 54 broker for trade of 100 shares at $50 per share is $33.77.
The value of confidence interval for population mean is
ˉx±zα2σ√n=33.77±4=(33.77−4,33.77+4)=(29.77,37.77) .
Thus, the 95% confidence interval for population mean is ($29.77, $37.77).
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Chapter 8 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
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