Answered: A company has analysed data for a…

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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Question

A company has analysed data for a sample of employees who have undertaken training designed to improve their performance in completing a timed task. For each employee in the sample, data shows the time taken to perform the task before training and the time taken post training.

The data was used to construct a 95% confidence interval for the mean difference in time taken (before - after), and the interval was (6,10) minutes. Which of the following inferences is correct?

Select one:

a.The confidence interval indicates that there could be no difference, on average, between the time it takes to perform the task after training and before training.

b.We are 95% confident that the time taken to perform the task is lower after training than before training, on average.

c.We are 95% confident that the mean reduction in the time taken to perform the task after training is 8 minutes.

d.We are 95% confident that everyone doing the training will then be able to perform the task at least 6 minutes faster.

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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