A new company is manufacturing light bulbs. The CEO claims that the average light bulb lasts 260 days. A researcher selects 25 bulbs for testing. The sample bulbs last an average of 250 days with a standard deviation of 20 days. If the CEO's claim was true, can we conclude that 25 random bulbs will last 260 days at a 0.01 level of significance?
Can you explain the steps in getting the answer?