Electrical vehicle (EV) batteries come with a warranty of six years or 160,000km equivalent. However, car manufacturers believe that electric car battery life is more than 200,000 kilometres. To test if this belief is correct, a random sample of 400 batteries is tested and their lifetime is recorded. The sample mean of lifetime was found to be 210,000 kilometres. Assume that lifetime is normally distributed with a population standard deviation of 150,000 kilometres. Conduct a hypothesis test to find out whether car manufacturers belief is true at 1% significant level