Answered: An experiment is conducted to estimate…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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An experiment is conducted to estimate the difference in work productivity for employees under two conditions: with and without music playing in the background. Twenty employees volunteered to be part of the study. Ten of the volunteers were randomly assigned to work for one week with music playing in the background. The other 10 volunteers worked for one week without music playing in the background. Productivity is measured by counting the number of units produced for the week. A 99% confidence interval for the difference in the population means is (1.525, 7.275). What is the interpretation of this interval?

We can be 99% confident that between 1.525 and 7.275 additional employees were productive while working without music playing in the background versus working with music playing in the background.

We can be 99% confident that between 1.525 and 7.275 fewer employees were productive while working without music playing in the background versus working with music playing in the background.

We can be 99% confident that the true difference in the population mean number of units produced by all employees who work without listening to music for one week is about 1.525 to 7.275 units greater than the mean number of units produced by all employees who work while listening to music for one week.

We can be 99% confident that the difference in the mean number of units produced by the 10 employees who worked without listening to music for one week is about 1.525 to 7.275 units greater than the mean number of units produced by the 10 employees who worked while listening to music for one week.

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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