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

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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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

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