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Name: The manufacturer of the X-15 steel-belted redial truck tire claims tha
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Description: The manufacturer of the X-15 steel-belted redial truck tire claims that the mean mileage the tire can be driven before the tread wears out is at least 60,000 miles. Crosset Truck Company bought a sample of 48 tires and found that the mean mileage for

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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The manufacturer of the X-15 steel-belted redial truck tire claims that the mean mileage the tire can be driven before the tread wears out is at least 60,000 miles. Crosset Truck Company bought a sample of 48 tires and found that the mean mileage for its trucks is 59,000 miles (i.e. less than the manufacturer’s claim) with a standard deviation of 5,000 miles. 1) Test the manufacturer’s claim at a significance level (α) equals 5%. 2) Would your answer in part (1) change if the probability of type I error equals zero? Justify your answer. 3) Would your answer in (1) change if the confidence level changes to be 99%. Justify your answer with proper test. 4) Another engineer has argued that tiers are considered to be fully consumed after 120000 mileage, test this claim at significance level of 10%. 5) If the manager of a store is thinking about establishing a new billing system for the store's credit costumers. After a thorough financial analysis, she determines that the new system will be cost effective only if the mean monthly income is more than 170£. A random sample of 400 monthly accounts is drawn, for which the sample mean is 178£. The manager knows that the accounts are normally distributed with standard deviation of 65£. Can the manager conclude from this that the new system will be cost-effective at significance level (α) equals 5%.?

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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