A tire company claims that the lifetimes of its tires average 50500 miles. The standard deviation of tire lifetimes is known to be 5500 miles. You sample 150 tires and will test the hypothesis that the mean tire lifetime is at least 50500 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 50000 miles. a) It is decided to reject H0 if the sample mean is less than 49900. Find the level and power of this test. Round the answers to four decimal places.The level is _____.The power is _____.b) If the test is made at the 5% level, what is the power? Round the answer to four decimal places.The power is _______ .c) At what level should the test be conducted so that the power is 0.85? The level is ____.

Answered: A tire company claims that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A tire company claims that the lifetimes of its tires average 50500 miles. The standard deviation of tire lifetimes is known to be 5500 miles. You sample 150 tires and will test the hypothesis that the mean tire lifetime is at least 50500 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 50000 miles.

a) It is decided to reject H₀ if the sample mean is less than 49900. Find the level and power of this test. Round the answers to four decimal places.

The level is _____.

The power is _____.

b) If the test is made at the 5% level, what is the power? Round the answer to four decimal places.

The power is _______ .

c) At what level should the test be conducted so that the power is 0.85?

The level is ____.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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