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Name: A metropolitan transportation authority has set a bus mechanical relia
Uploaded: 2024-03-20T07:07:12.000Z
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Description: A metropolitan transportation authority has set a bus mechanical reliability goal of 3,700 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted

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 metropolitan transportation authority has set a bus mechanical reliability goal of 3,700 bus miles. Bus mechanical reliability is measured specifically as the number of bus miles between mechanical road calls. Suppose a sample of 100 buses resulted in a sample mean of 3,750 bus miles and a sample standard deviation of 175 bus miles.

a. Is there evidence that the population mean bus miles is more than

3,700 bus miles? (Use a 0.10 level of significance.)

1) State the null and alternative hypotheses.

2) Identify the critical value(s).

3) Determine the test statistic and the P value

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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Step 1

Given information:

A metropolitan transportation authority has set a bus mechanical reliability goal of $μ = 3700 bus miles$ .

A sample of n = 100 buses is randomly taken.

Sample mean, $\bar{x} = 3750 bus miles$

Sample standard deviation, s = 175 bus miles

Level of significance = 0.10

It is required to check whether there is evidence that the population mean bus miles is more than 3700 bus miles or not.

1) To state the null and alternative hypotheses

2) To identify the critical value (s)

3) To determine the test statistic and the p value

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