A company that makes robotic vacuums claims their newest model of vacuum lasts, on average, 2 hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of 5 vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. They would like to know if there is convincing evidence that the true mean run time differs from 2 hours. The consumer group plans to test the hypotheses  = 2 versus < 2, where μ = the true mean run time for all vacuums of this model. The power of this test to reject  = 2 when μ = 1.75 is 0.0865 using a significance level of 0.05. Which combination of sample size and significance level would increase the power of this test the most?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
Question

A company that makes robotic vacuums claims their newest model of vacuum lasts, on average, 2 hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of 5 vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. They would like to know if there is convincing evidence that the true mean run time differs from 2 hours. The consumer group plans to test the hypotheses  = 2 versus < 2, where μ = the true mean run time for all vacuums of this model.

The power of this test to reject  = 2 when μ = 1.75 is 0.0865 using a significance level of 0.05. Which combination of sample size and significance level would increase the power of this test the most?

 
 
 
 
A company that makes robotic vacuums claims their
newest model of vacuum lasts, on average, 2 hours
when starting on a full charge. To investigate this claim,
a consumer group purchases a random sample of 5
vacuums of this model. They charge each unit fully and
then measure the amount of time each unit runs. They
would like to know if there is convincing evidence that
the true mean run time differs from 2 hours. The
consumer group plans to test the hypotheses Ho: H = 2
versus H: μ< 2, where μ = the true mean run time for
all vacuums of this model.
The power of this test to reject Ho: μ = 2 when μ = 1.75
is 0.0865 using a significance level of 0.05. Which
combination of sample size and significance level
would increase the power of this test the most?
O n = 10, α = 0.01
O n = 10, α = 0.10
On=20, α = 0.01
O n=20, α = 0.10
Transcribed Image Text:A company that makes robotic vacuums claims their newest model of vacuum lasts, on average, 2 hours when starting on a full charge. To investigate this claim, a consumer group purchases a random sample of 5 vacuums of this model. They charge each unit fully and then measure the amount of time each unit runs. They would like to know if there is convincing evidence that the true mean run time differs from 2 hours. The consumer group plans to test the hypotheses Ho: H = 2 versus H: μ< 2, where μ = the true mean run time for all vacuums of this model. The power of this test to reject Ho: μ = 2 when μ = 1.75 is 0.0865 using a significance level of 0.05. Which combination of sample size and significance level would increase the power of this test the most? O n = 10, α = 0.01 O n = 10, α = 0.10 On=20, α = 0.01 O n=20, α = 0.10
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt