We consider the problem of improving lithium car batteries. A research group is makıng great advances using a new type anode and they claim that the mean life is greater than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject them to recharge cycles until they fail. The claim will be established if the sample mean lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further improvements are needed. Assume that the population standard deviation o = 192 cycles is known. (a) Find the probability of a Type I error. (b) Find the probability of a Type II error when µ = 1680 cycles.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question
We consider the problem of improving lithium car batteries. A research group is
makıng great advances using a new type anode and they claim that the mean life is greater
than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject
them to recharge cycles until they fail. The claim will be established if the sample mean
lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further
improvements are needed. Assume that the population standard deviation o = 192 cycles
is known.
(a)
Find the probability of a Type I error.
(b)
Find the probability of a Type II error when u = 1680 cycles.
Transcribed Image Text:We consider the problem of improving lithium car batteries. A research group is makıng great advances using a new type anode and they claim that the mean life is greater than 1600 recharge cycles. To support this claim, they create 36 new batteries and subject them to recharge cycles until they fail. The claim will be established if the sample mean lifetime is greater than 1640 cycles. Otherwise, the claim will not be established and further improvements are needed. Assume that the population standard deviation o = 192 cycles is known. (a) Find the probability of a Type I error. (b) Find the probability of a Type II error when u = 1680 cycles.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman