Question

A sample survey of 56 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.88. 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

Answer 1

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

Margin of Error = Z * (Population Standard Deviation / √Sample Size)

Where Z represents the critical value for the desired confidence level. For a 95% confidence level, the Z-value is approximately 1.96.

Given the population standard deviation of $14 and a sample size of 56, we can substitute these values into the formula:

Margin of Error = 1.96 * (14 / √56) ≈ 3.64

Therefore, the margin of error associated with a 95% confidence interval is approximately $3.64.

b. 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 can use the following formula:

Confidence Interval = Sample Mean ± Margin of Error

The sample mean is given as $33.88, and the margin of error we calculated in part (a) is approximately $3.64.

Confidence Interval = $33.88 ± $3.64

Therefore, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is approximately ($30.24, $37.52).

I hope this helps!!