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You measure the lifetime of a random sample of 64 tires of a certain brand. The sample mean is x = 50 months. Suppose that the lifetimes for tires of this brand follow a normal distribution, with unknown mean and true standard deviation of 5 kg. Create a 99% confidence interval for the mean lifetime of this brand of tires. Interpret the interval in the context of the problem. Suppose the tire company claimed this brand of tires will last 55 months. Consumer reports wants to test to see if the company is telling the truth about these tires and took the sample that we received above. Preform the hypothesis test in its entirety, being sure to use context in the conclusion. Use alpha=0.01. Do you confidence interval in 6 and hypothesis test in 7 agree? Why or why not?

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