1. A systems engineer is assigned a task of checking if the hospital has to switch to product costing method. There are two types of patients, A and B. The engineer has collected 10 data points for each type, representing the times they consume for the service. The times are given below, in hours:

Type A 0.45 0.30 1.00 1.20 1.40 0.25 0.50 0.70 2.10 1.20

Type B 2.20 1.60 1.40 0.90 2.50 1.40 0.20 0.30 1.80 3.20

The process costs $300 per hour. The product costing will be recommended only if costs for the two types are significantly different. Conduct a t-test to check if there is any significant difference in the costs for the two populations.

Use an alpha value of 0.05. Define H0 and H1 clearly.