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Question: a computer company claims that the batteries in its laptops...

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A computer company claims that the batteries in its laptops last 4 hours on average. A consumer report firm gathered a sample of 16 batteries and conducted tests on this claim. The sample mean was 3 hours 50 minutes, and the sample standard deviation was 20 minutes. Assume that the battery time distribution as normal.

  1. Test if the average battery time is shorter than 4 hours at α = 0.05. Use the 5-step method.
  2. b) Construct a 95% confidence interval of the mean battery time.
  3. c) If you were to test H0: µ =240 minutes vs. H1: µ ≠ 240 minutes, what would you conclude from your result in part (b)?

    d) Suppose that a further study establishes that, in fact, e population mean is 4 hours. Did the test in part (c) make a correct decision? If not, what type of error did it make?

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