A manufacturer of light bulbs advertises that, on average, its long-life bulb will last more than 5300 hours. To test this claim, a statistician took a random sample of 81 bulbs and measured the amount of time until each bulb burned out. The mean lifetime of the sample 5389 hours and has a standard deviation of 430 hours. Can we conclude with 99% confidence that the claim is true? Fill in the requested information below. (a) The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (−[infinity],a) is expressed (-infty, a), an answer of the form (b,[infinity]) is expressed (b, infty), and an answer of the form (−[infinity],a)∪(b,[infinity]) is expressed (-infty, a) ∪(b, infty). (b) The rejection region for the standardized test statistic: (c) Your decision for the hypothesis test: A. Do Not Reject H1​. B. Reject H0​. C. Reject H1​. D. Do Not Reject H0​.