The life in hours of a thermocouple used in a furnace is known to be approximately...

The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with σ=20 hours. A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539, 529.

Is there evidence to support the claim that mean life exceeds 540 hours? Use a fixed-level test with =0.05.
What is the P-value for this test?
What is the -value for this test if the true mean life is 560 hours?
What sample size would be required to ensure that does not exceed 0.10 if the true mean life is 560 hours?
Construct a 95% one-sided lower CI on the mean life.
Use the CI found in part (e) to test the hypothesis.

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