# Probability of Type II error

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## A tire manufacturer produces tires that are believed to have a mean life of at least 25,000 miles when

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Question: A tire manufacturer produces tires that are believed to have a mean life of at least 25,000 miles when the production process is working correctly. Based on past experience, the population standard deviation of the lifetime of the tires is 3,500 miles. Assume a level of significance for testing of 5%, and a random sample of 100 tires:
A) What would be the consequences of making a Type II error in this problem?
B) Compute the Probability of making a Type II error if the true population mean is 24,000 miles

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## 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  = $\sigma&space;=&space;20$ 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.