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In a study of the lifetimes of electronic components, a
Chapter 5, Problem 16SE(choose chapter or problem)
In a study of the lifetimes of electronic components, a random sample of 400 components are tested until they fail to function. The sample mean lifetime was 370 hours and the standard deviation was 650 hours. True or false:
An approximate 95% confidence interval for the mean lifetime of this type of component is from 306.3 to 433.7 hours. About 95% of the sample components had life- times between 306.3 and 433.7 hours. If someone takes a random sample of 400 components, divides the sample standard deviation of their lifetimes by 20, and then adds and subtracts that quantity from the sample mean, there is about a 68% chance that the interval so constructed will cover the mean lifetime of this type of component. The z table can’t be used to construct confidence intervals here, because the lifetimes of the components don’t follow the normal curve.About 68% of the components had lifetimes in the interval 370 \(\pm\) 650 hours.
Equation transcription:
Text transcription:
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Questions & Answers
QUESTION:
In a study of the lifetimes of electronic components, a random sample of 400 components are tested until they fail to function. The sample mean lifetime was 370 hours and the standard deviation was 650 hours. True or false:
An approximate 95% confidence interval for the mean lifetime of this type of component is from 306.3 to 433.7 hours. About 95% of the sample components had life- times between 306.3 and 433.7 hours. If someone takes a random sample of 400 components, divides the sample standard deviation of their lifetimes by 20, and then adds and subtracts that quantity from the sample mean, there is about a 68% chance that the interval so constructed will cover the mean lifetime of this type of component. The z table can’t be used to construct confidence intervals here, because the lifetimes of the components don’t follow the normal curve.About 68% of the components had lifetimes in the interval 370 \(\pm\) 650 hours.
Equation transcription:
Text transcription:
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ANSWER:Answer:
Step 1 of 5:
(a)
In this question, we are asked to state the True or false for given statements.
Statement: an approximate confidence interval for the mean lifetime of this type of component is from
.
Given a random sample of 400 components are tested. The sample mean lifetime was and the standard deviation was
.
Let be a large sample of size
from a population with mean
and standard deviation
then a level confidence interval for
is
Since we want 95% confidence interval, then a level is
and
Then for
is
, hence
Hence an approximate confidence interval for the mean lifetime of this type of component is from
.
The statement is true.