Answered: Hours Actually Worked. In the article…

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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Hours Actually Worked. In the article “How Hours of Work Affect Occupational Earnings” (Monthly Labor Review, Vol. 121), D. Hecker discussed the number of hours actually worked as opposed to the number of hours paid for. The study examines both full-time men and full-time women in 87 different occupations. According to the article, the mean number of hours (actually) worked by female marketing and advertising managers is µ = 45 hours. Assuming a standard deviation of σ = 7 hours, decide whether each of the following statements is true or false or whether the information is insufficient to decide. Give a reason for each of your answers.

a. For a random sample of 196 female marketing and advertising managers, chances are roughly 95% that the sample mean number of hours worked will be between 31 hours and 59 hours.
b. Approximately 95% of all possible observations of the number of hours worked by female marketing and advertising managers lie between 31 hours and 59 hours.
c. For a random sample of 196 female marketing and advertising managers, chances are roughly 95% that the sample mean number of hours worked will be between 44 hours and 46 hours.

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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