Question

As part of an annual review of its accounts, a discount brokerage selects a random sample of 30 customers. Their accounts are reviewed for total account valuation, which showed a mean of $36,900, with a sample standard deviation of $8,250. (Use tDistribution Table.)

What is a 98% confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount.)

Answer 1

The sample size is 30.

The sample mean is $36,900.

The sample standard deviation is $8,250.

The confidence level is 98%.

The critical value for a 98% confidence interval with 29 degrees of freedom is 2.457.

The confidence interval is calculated as follows:

(Sample mean - t-critical value * sample standard deviation / sqrt(sample size), Sample mean + t-critical value * sample standard deviation / sqrt(sample size))

(36,900 - 2.457 * 8,250 / sqrt(30), 36,900 + 2.457 * 8,250 / sqrt(30))

(21,668.25, 52,131.75)

Therefore, a 98% confidence interval for the mean account valuation of the population of customers is $21,668.25 to $52,131.75.

Explanation: