Step 1 :Convert the weight of the dog from pounds to kilograms using the conversion factor 1 lb = 0.45 kg. The calculation is \(65 \, \text{lb} \times 0.45 \, \text{kg/lb} = 29.25 \, \text{kg}\).
Step 2 :Calculate the amount of medicine required using the dosage of 8 mg per kilogram of the animal's mass. The calculation is \(29.25 \, \text{kg} \times 8 \, \text{mg/kg} = 234 \, \text{mg}\).
Step 3 :\(\boxed{234 \, \text{mg}}\) is the amount of medicine Jane should give her dog.