Question

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. The survey is conducted annually. WIth the histiorical data available, assume a known population standard deviation of $15.

a. Using the sample datta, what is the margin of error associated with a 95% confidence interval?
b. Develop 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.

Answer 1

The margin of error associated with a 95% confidence interval is $4.14. The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.63, $38.91).

Step-by-step explanation:

To calculate the margin of error associated with a 95% confidence interval, we need to use the formula:

Margin of Error = Z * (σ / √n)

Where:

• Z is the Z-score for the desired confidence level (95% confidence level corresponds to a Z-score of 1.96)
• σ is the population standard deviation ($15 in this case)
• n is the sample size (54 in this case)

Substituting the values into the formula, we get:

Margin of Error = 1.96 * (15 / √54) = 4.14

Therefore, the margin of error associated with a 95% confidence interval is $4.14.

To develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share, we use the formula:

Confidence Interval = Sample Mean ± Margin of Error

Substituting the values into the formula, we get:

Confidence Interval = $33.77 ± $4.14 = ($29.63, $38.91)

Therefore, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.63, $38.91).