uppose Laura, a facilities manager at a health and wellness company, wants to estimate the difference in the average amount of time that men and women spend at the company's fitness centers each week. Laura randomly selects 13 adult male fitness center members from the membership database and then selects 13 adult female members from the database. Laura gathers data from the past month containing logged time at the fitness center for these members. She plans to use the data to estimate the difference in the time men and women spend per week at the fitness center. The sample statistics are summarized in the table. Population Population description Population mean (unknown) Sample size Sample mean (min) Sample standard deviation (min) 1 male ?1 ?1=13 ?⎯⎯⎯1=132.5 ?1=45.3 2 female ?2 ?2=13 ?⎯⎯⎯2=108.7 ?2=31.1 df=21.256 The population standard deviations are unknown and unlikely to be equal, based on the sample data. Laura plans to use the two-sample ?-procedures to estimate the difference of the two population means, ?1−?2. First, compute the estimated standard error, SE, of the difference in the sample means that Laura uses to construct the confidence interval. Provide your answer precise to at least three decimal places. SE= min Next, compute the margin of error, ?, for the 95% confidence interval for the difference of the population means using software or a table of ?-distributions. Provide your answer precise to at least one decimal place. ?= min

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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uppose Laura, a facilities manager at a health and wellness company, wants to estimate the difference in the average amount of time that men and women spend at the company's fitness centers each week.

Laura randomly selects 13 adult male fitness center members from the membership database and then selects 13 adult female members from the database. Laura gathers data from the past month containing logged time at the fitness center for these members. She plans to use the data to estimate the difference in the time men and women spend per week at the fitness center. The sample statistics are summarized in the table.

Population	Population description	Population mean (unknown)	Sample size	Sample mean (min)	Sample standard deviation (min)
1	male	?1	?1=13	?⎯⎯⎯1=132.5	?1=45.3
2	female	?2	?2=13	?⎯⎯⎯2=108.7	?2=31.1

df=21.256

The population standard deviations are unknown and unlikely to be equal, based on the sample data. Laura plans to use the two-sample ?-procedures to estimate the difference of the two population means, ?1−?2.

First, compute the estimated standard error, SE, of the difference in the sample means that Laura uses to construct the confidence interval. Provide your answer precise to at least three decimal places.

SE=

min

Next, compute the margin of error, ?, for the 95% confidence interval for the difference of the population means using software or a table of ?-distributions. Provide your answer precise to at least one decimal place.

?= min

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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