The life in hours of an electronic sensor is known to be approximately Normally distributed

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Question:

The life in hours of an electronic sensor is known to be approximately Normally distributed, with population standard deviation  = \sigma = 20 hours. A random sample of 10 sensors resulted in the following data: 500,550,560,575,525,505,510,540,550,545.

  • Is there evidence to support the claim that mean life exceeds 520 hours? Use a fixed-level test with alpha = 0.05.
  • What is the P-value of this test? Conclude the same of part (a)?
  • What is the Beta-value for this test if the true mean life is 535 hours?
  • What sample size would be required to ensure that Beta does not exceed 0.10 if the true mean life is 540 hours?
  • Construct a 95% one-sided lower CI on the mean life.
  • Use the CI found in part e) to test the hypothesis.

We are given that the life in hours of an electronic sensor is approximately Normally distributed with population standard deviation  = \sigma = 20  .

We have following random sample of size 10:  500,550,560,575,525,505,510,540,550,545.

Part a) We have to test claim that mean life exceeds 520 hours at 0.05 significance level.

Claim: mean life exceeds 520 hours.

Step 1) State H0 and H1:

H_{0}: \mu = 520 \: \: Vs \: \: H_{1}: \mu > 520