The president of a large bank with many branch offices wanted to know if the quality of customer service at a new branch office was acceptable. One aspect of service that was examined was the length of time that customers had to wait in line before being helped by a member of the bank’s staff. The bank decided on acceptable probabilities for the waiting-time categories, and these are given in the table below. A table is shown with two columns labeled waiting time category and probability. The first column reads no more than 1 minute, more than 1 minute but no more than 3 minutes, more than 3 minutes but no more than 5 minutes, more than 5 minutes but no more than 10 minutes, and more than 10 minutes. The second column reads 0.3, 0.25, 0.20, 0.15, and 0.1.

To investigate whether the quality of customer service was acceptable, waiting times were recorded for a random sample of 100 customers at the new branch office. The table below shows the numbers of customers observed in the five waiting-time categories.

A table is shown with two columns labeled waiting time category and number of customers. The first column reads no more than 1 minute, more than 1 minute but no more than 3 minutes, more than 3 minutes but no more than 5 minutes, more than 5 minutes but no more than 10 minutes, more than 10 minutes, and total. The second column reads 25, 21, 21, 20, 13, and 100.

Use the sample data for the 100 customers to conduct a statistical test to determine if the waiting times at the new branch office are inconsistent with the acceptable probabilities for the waiting-time categories.