Answered: Test a claim that the mean amount of…

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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Question

Test a claim that the mean amount of carbon monoxide in the air in U.S cities is less than 2.33 parts per million. It was found that the mean amount of carbon monoxide in the air for the random sample of 63 cities is 2.38 parts per millionband the standard deviation is 2.12 parts per million. At a= 0.01, can the claim be supported? Assume population is normally distributed.

i) Identify the claim and state Ho and Ha

ii) Find the critical value(s) and identify the rejection region(s).

iii) Find the standardized test statistic, t.

iv) Decide wheter to reject or fail to reject the null hypothesis.

v) Interpret the decision in the context if the original claim.

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**Hypothesis Testing Steps**

ii) **Find the critical value(s) and identify the rejection region(s).**

iii) **Find the standardized test statistic, \( t \).**

iv) **Decide whether to reject or fail to reject the null hypothesis.**

v) **Interpret the decision in the context of the original claim.**

**Choose the correct answer.**

a)

i)

\( H_0 \)

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This segment guides users through the process of hypothesis testing, from determining critical values and test statistics to making informed decisions about the null hypothesis.

Test a claim that the mean amount of carbon monoxide in the air in U.S. cities is less than 2.33 parts per million. It was found that the mean amount of carbon monoxide in the air for the random sample of 63 cities is 2.38 parts per million and the standard deviation is 2.12 parts per million. At α = 0.01, can the claim be supported? Complete parts (i) through (v) below. Assume the population is normally distributed.

i) Identify the claim and state

\( H_0 \)

and

\( H_a \)

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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