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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Test a claim that the mean amount of lead in the air in U.S, cites is less than 0.087 microgram per cubic meter. it was found that the mean amount of lead in the air for the random sample of 58 US, ottes is OCSS microgram per cubic meter and the standard deviation is 0.068 microgram per cudie meter. At a = 0. 10, can the claim be supported? Complete parts (a) through (e) below. Assume the population is nomally distributed. (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are t0=______(Use a comma to separate answers as needed. Round to two decimal places as needed.) (c) Find the standardized test statistic, t. The standardized test statistic is t=______(Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. (Reject ,Fail to reject)_____H0 because the standardized test statistic_______(is ,is not), in the rejection region. (e) Interpret the decision in the context of the original claim. There______(is, is not), enough evidence at the ___ % level of significance to ____(reject, support) the claim that the mean amount of lead in the air in U.S. cities is _______( less than, greater than or equal, equal, not equal, less than or equal, greater than) ____(Type integers or decimals. Do not round.) microgram per cubic meter.

**Hypothesis Testing of Mean Lead Levels in U.S. Cities**

**Problem Statement:**
Test a claim that the mean amount of lead in the air in U.S. cities is less than 0.037 microgram per cubic meter. A random sample of 58 U.S. cities shows a mean of 0.038 microgram per cubic meter with a standard deviation of 0.068 microgram per cubic meter. Perform the test at a significance level of α = 0.10. Assume the population is normally distributed.

**Part (a): Identify the claim and state \( H_0 \) and \( H_a \)**
- Null Hypothesis (\( H_0 \)): \( \mu \geq 0.037 \)
- Alternative Hypothesis (\( H_a \)): \( \mu < 0.037 \)

The claim is the alternative hypothesis.

**Part (b): Find the critical value(s) and identify the rejection region(s)**

- The critical value(s) \( t_0 \) is/are [Box for input].
- Instruction: Round to two decimal places as needed.

*Methodology:*
- The solution involves identifying the critical t-value from the t-distribution table for a one-tailed test at α = 0.10.
- Determine the rejection region using critical value(s).

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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