# Hypothesis testing for Mean

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## Last month the waiting time at the drive through window of a fast-food restaurant was 3.7 minutes

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Question:

Last month the waiting time at the drive-through window of a fast-food restaurant was 3.7 minutes. The franchise has installed a new process intended to reduce waiting time. After the installation, a random sample of 64 orders is selected. The sample mean waiting time is 3.57 minutes with a sample standard deviation of 0.8 minutes. At a 5% level of significance, is there sufficient evidence that the population mean waiting time is now less than 3.7 minutes? What is your conclusion?

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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.