A manufacturer of light bulbs advertises that, on average, its long-life bulb will last more than 5,000 hours. To test the claim, a statistician took a random sample of 100 bulbs and measured the amount of time until each bulb burned out. The sample mean was calculated as = 5,064 hours. If we assume that the lifetime of this type of bulb has a standard deviation of 400 hours, can we conclude at the 5% significant level that the claim is true?