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. Assuming σ is unknown, calculate a 90% confidence interval on the standard deviation (σ) of the wear-out times for the population of running shoes.
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.
Assuming σ is unknown, calculate a 90% confidence interval on the standard deviation (σ) of the wear-out times for the population of running shoes.
In statistical inference, there are two types of estimation,
1) Point estimation and
2) Interval estimation.
If an interval is proposed as an estimate of the unknown parameter, then it is interval estimation. An interval (T1, T2) that is proposed to contain the unknown parameter is called a confidence interval.
The data are given,
Level of significance = = 1-90% = 1-0.90 = 0.10
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