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Name: Marta Human Resource manager has asserted that Marta workers work, on
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Description: Marta Human Resource manager has asserted that Marta workers work, on average, no more than three hours of overtime per week. Let assume that overtime hour is normally distributed with a standard deviation of 1.2 hours. The union leaders believe that

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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Marta Human Resource manager has asserted that Marta workers work, on average, no more than three hours of overtime per week. Let assume that overtime hour is normally distributed with a standard deviation of 1.2 hours. The union leaders believe that this assertion is incorrect and that the actual mean overtime is more than three hours per week. The union leaders decide to test this claim and claim their conclusion on the sample result. They conduct a study on a sample of payroll records for 250 employees.

The payroll records produced a sample mean of 3.15 hours. Do the union leaders have a basis for a grievance against Marta? Support your answer with a relevant statistical procedure.

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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