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.