Answered: The 2008 Workplace Productivity Survey,…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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1. Interval estimation of a population mean, population standard deviation known

The 2008 Workplace Productivity Survey, commissioned by LexisNexis and prepared by WorldOne Research, included the question, “How many work-related e-mails do you receive during the typical workday?” Let x = the number of work-related e-mails a legal professional receives during a typical workday. Suppose that x is normally distributed with a known standard deviation of 24.3.

A sample of 250 legal professionals was surveyed, and the sample’s mean response was 36.7 e-mails. Use the sample information to estimate μ, the mean number of work-related e-mails a legal professional receives during a typical workday.

The sampling distribution of x̄ x̄ is normal with a mean _____ and a standard deviation ______ .

Use the following Distributions tool to develop a 99% confidence interval estimate of the mean number of work-related e-mails a legal professional receives during a typical workday.

You can be 99% confident that the interval estimate _____ to ______ includes the population mean µ.

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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