To test the durability of the material used for running shoes, a sample is placed in testing device that simulates an average-sized person using the shoes until the material wears out. The material is supposed to last at least an average of 20 months. Suppose that the wear-out time is characterized by a normal distribution with both μ and σ unknown. A test on five randomly selected pairs of shoes yields wear-out times of 20, 28, 18, 24, and 25 months. If the mean shoe wear-out time of the sample is is 22 months, what is the probability you would correctly reject the null hypothesis μ = 20 versus the alternative μ > 20 assuming that the population is normal and now also assuming that σ = 4 is known? Stated differently, what is the power for μa = 22.
To test the durability of the material used for running shoes, a sample is placed in testing device that simulates an average-sized person using the shoes until the material wears out. The material is supposed to last at least an average of 20 months. Suppose that the wear-out time is characterized by a
A test on five randomly selected pairs of shoes yields wear-out times of 20, 28, 18, 24, and 25 months.
If the mean shoe wear-out time of the sample is is 22 months, what is the probability you would correctly reject the null hypothesis μ = 20 versus the alternative μ > 20 assuming that the population is normal and now also assuming that σ = 4 is known? Stated differently, what is the power for μa = 22.
The null hypothesis:
H0: μ = 20
Versus the alternative hypothesis:
Ha: μ > 20
Assuming that the population is normal and σ is known.
σ = 4
We have to find the power for μa = 22.
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