Question

A sample survey of 52 discount brokers showed that the mean price charged for a trade of 100 shares at 50 per share was 33.9. The survey is conducted annually. With the historical data available, assume a known population standard deviation of 14.

a. Using the sample data, what is the margin of error associated with a 95% confidence interval (to 2 decimals)?

b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at ¥50 per share (to 2 decimals).

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Answer 1

a)

- Margin of error E = Z/2 * / sqrt(n)

= 1.96 * 14 / sqrt(52)

= 3.81

b)

95% confidence interval for is

- Z/2 * / sqrt(n)  < < + Z/2 * / sqrt(n)

33.9 - 3.81 < < 33.9 + 3.81 (3.81 is margin of error calculated in part a)

30.09 < < 37.71

95% CI is (30.09 , 37.71)