Question

As part of a quality improvement program, your mail-order company is evaluating the process of filling customer orders. According to company standards, an order is shipped on time if it is sent within two working days of the time it is received. You select an SRS of 201 of the 6,000 orders received in the past month for an audit. The audit reveals that 109 of these orders were shipped on time.

What is the upper endpoint of a 99% confidence interval for p, the population proportion of orders in the last month that were shipped on time?

(Apply the large-sample confidence interval procedure. You will need to calculate z* in Excel, and do not round in your intermediate calculations.)

Express your answer in decimal form to two decimal places of accuracy.

Answer 1

From standard normal tables, we have here:
P( -2.576 < Z < 2.576) = 0.99

The sample proportion here is computed as:
p = x/n = 109/6000 = 0.0182

The upper endpoint of the confidence interval for p here is computed as:

This is the required upper endpoint for the 99% confidence interval for the population proportion of orders last month that were shipped on time.