8. A confidence interval for estimating the mean Distributions1 2The psychologist can be 95% confident that the interval fromv toincludes the unknown population mean u.Normally the psychologist will not know the value of the population mean. But consider the (unrealistic) scenario that a census of legal professionals isconducted. The census reveals that the population mean is u = 41.2.How would the psychologist most likely react to the news?O The psychologist would be surprised that p = 41.2, because that value is outside the confidence interval.O The psychologist would not be surprised that µ = 41.2, because that value is inside the confidence interval.O The psychologist would be surprised that p = 41.2, because that value is inside the confidence interval.O The psychologist would not be surprised that u = 41.2, because that value is outside the confidence interval. An industrial/organizational psychologist wants to improve worker productivity for a client firm, but first she needs to gain a better understanding ofthe life of the typical white-collar professional. Fortunately, she has access to the 2008 Workplace Productivity Survey, commissioned by LexisNexisand prepared by WorldOne Research, which surveyed a sample of 650 white-collar professionals (250 legal professionals and 400 other professionals).One of the survey questions was, "How many work-related emails do you receive during a typical workday?" For the subsample of legal professionals(n = 250), the mean response was M = 36.7 emails, with a sample standard deviation of s = 24.3 emails.The estimated standard error is SM =Use the following Distributions tool to develop a 95% confidence interval estimate of the mean number of work-related emails legal professionalsreceive during a typical workday.Select a DistributionDistributions1

Given Data : Sample Size, n = 250 Sample Mean, x̄ = 36.7 standard deviation, s = 24.3 Significance level, α =1- 0.95 = 0.05Solution : A) The estimated standard error is SM = s/√n = 24.3/√250 = 1.5369B) 95% confidence interval : Degree of freedom df = n-1 = 250 - 1 =249 Point estimate: x̄ = 36.7 critical value at α=0.05 with df =249 is tα/2,df=1.97 .....from student's t distribution table Margin of error: ME=tα/2,df * S/√n =1.97 × 24.3/√250 = 3.0276 Margin of error is 3.0276 Now 95% confidence interval is CI=point estimate ± ME =36.7 ± 3.0276 (36.7-3.0276 , 36.7+3.0276)s = (33.6724, 39.7276) The psychologist can be 95% confident that the interval from 33.6724 to 39.7276 includes the unknown population mean u.C) The psychologist would be surprised that u = 41.2, because that value is outside the confidence interval.

Answered: The psychologist can be 95% confident…

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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8. A confidence interval for estimating the mean

Distributions
1 2
The psychologist can be 95% confident that the interval from
v to
includes the unknown population mean u.
Normally the psychologist will not know the value of the population mean. But consider the (unrealistic) scenario that a census of legal professionals is
conducted. The census reveals that the population mean is u = 41.2.
How would the psychologist most likely react to the news?
O The psychologist would be surprised that p = 41.2, because that value is outside the confidence interval.
O The psychologist would not be surprised that µ = 41.2, because that value is inside the confidence interval.
O The psychologist would be surprised that p = 41.2, because that value is inside the confidence interval.
O The psychologist would not be surprised that u = 41.2, because that value is outside the confidence interval.

An industrial/organizational psychologist wants to improve worker productivity for a client firm, but first she needs to gain a better understanding of
the life of the typical white-collar professional. Fortunately, she has access to the 2008 Workplace Productivity Survey, commissioned by LexisNexis
and prepared by WorldOne Research, which surveyed a sample of 650 white-collar professionals (250 legal professionals and 400 other professionals).
One of the survey questions was, "How many work-related emails do you receive during a typical workday?" For the subsample of legal professionals
(n = 250), the mean response was M = 36.7 emails, with a sample standard deviation of s = 24.3 emails.
The estimated standard error is SM =
Use the following Distributions tool to develop a 95% confidence interval estimate of the mean number of work-related emails legal professionals
receive during a typical workday.
Select a Distribution
Distributions
1

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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