The mean lifetime of a random sample of 80 light bulbs produced by a factory is found to be 1460 hours, with a standard deviation s = 110 hours. The manufacturer claims its light bulbs have a mean lifetime of 1500 hours. (i) Formulate the appropriate null and alternative hypotheses [0.5 marks] (ii) Test at the 0.05 and 0.01 levels of significance whether this evidence contradicts the claim [0.5 marks]