Answered: Diane Chen, the Human Resources Manager…

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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Diane Chen, the Human Resources Manager for a private college, is interested in examining the number of hours overtime worked by staff in one week. She took a sample of 6 staff, with the results given below. 2, 1, 4.5, 7, 8, 5 a) Is the number of hours overtime worked by staff in a week categorical or numerical variable. If the variable is numerical, determine whether the variable is discrete or continuous. In addition, determine the level of measurement (eg ratio or nominal scale). b) Calculate the sample mean of this sample. Include units. c) Calculate the sample standard deviation (correct to 3 decimal places). Include units. d) What must be assumed about the population distribution in order to calculate a confidence interval? Give a reason for your answer e) Using the sample mean and sample standard deviation (found in b and c) calculate the 90% confidence interval for the population mean overtime hours. Include a concluding statement. f) If one staff member claimed they worked 7 hours overtime, based on this sample should you take their statement as true? Why/ why not?

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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