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A laptop manufacturer advertises that its battery lasts an average of \(10\) hours. A tech reviewer tests 64 laptops and finds a sample mean of \(9.6\) hours with a standard deviation of \(1.2\) hours.
  1. Construct a \(99\pourcent\) confidence interval for the true mean battery life.
  2. Does the test support the manufacturer's advertisement at the 1\(\pourcent\) significance level?

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