Answered: We should use a z-test or a t-test?…

Name: The manufacturer of a particular brand of tires claims they average le
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Description: The manufacturer of a particular brand of tires claims they average less than 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 8,000 miles. A survey of tire owners was c

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 a particular brand of tires claims they average less than 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 8,000 miles. A survey of tire owners was conducted. From the 29 tires surveyed, the mean lifespan was 47000 miles. Using alpha = 0.05, can we prove that the data in inconsistent with the manufacturers claim?

a. We should use a z-test or a t-test? State the reason you choose that distribution.

b. State the null and alternative hypotheses

c. Calculate the test statistic value (round to 4 decimal places)

d. Determine the p-value (round to 4 decimal places). Sketch the graph, shade the region corresponding to p-value and label the test statistic

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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