Answer the following questions.The mean length of a work week for the population of workers was reported to be 45 hours. Suppose that we would like to take a current sample of workers to see whether the mean length of a work week has decreased from the previously reported 45 hours. Suppose a current sample of 100 workers provided a sample mean ( ̅) of 42 hours and sample standard deviation (s) of 10 hours. Use 5% significance level to test whether the mean length of a work week has decreased from the previously reported 45 hours.You have been asked to determine if male and female managers in a big company have the same level of education. Independent random samples were taken of 100 male managers and 100 female managers. For male managers, the sample mean was 16 years of schooling with sample standard deviation (s1) equals to 3. For female managers, the sample mean was 14 years of schooling with sample standard deviation (s2) equals to 4. Do you have any reason at the 5% significance level to think that male and female managers have the same level of education?

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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 mean length of a work week for the population of workers was reported to be 45 hours. Suppose that we would like to take a current sample of workers to see whether the mean length of a work week has decreased from the previously reported 45 hours. Suppose a current sample of 100 workers provided a sample mean ( ̅) of 42 hours and sample standard deviation (s) of 10 hours. Use 5% significance level to test whether the mean length of a work week has decreased from the previously reported 45 hours.
You have been asked to determine if male and female managers in a big company have the same level of education. Independent random samples were taken of 100 male managers and 100 female managers. For male managers, the sample mean was 16 years of schooling with sample standard deviation (s₁) equals to 3. For female managers, the sample mean was 14 years of schooling with sample standard deviation (s₂) equals to 4. Do you have any reason at the 5% significance level to think that male and female managers have the same level of education?

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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