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Statistics / Applied Statistics and Probability for Engineers 6 / Chapter 8.2 / Problem 37E

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

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Chapter 8, Problem 37E

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QUESTION:

The brightness of a television picture tube can be evaluated by measuring the amount of current required to achieve a particular brightness level. A sample of 10 tubes results in \(\bar{x}=317.2\) and \(s=15.7\). Find (in microamps) a 99% confidence interval on mean current required. State any necessary assumptions about the underlying distribution of the data.

Equation Transcription:

$\overline{x}=317.2$

$s=15.7$

Text Transcription:

x bar=317.2

s=15.7

Questions & Answers

QUESTION:

The brightness of a television picture tube can be evaluated by measuring the amount of current required to achieve a particular brightness level. A sample of 10 tubes results in \(\bar{x}=317.2\) and \(s=15.7\). Find (in microamps) a 99% confidence interval on mean current required. State any necessary assumptions about the underlying distribution of the data.

Equation Transcription:

$\overline{x}=317.2$

$s=15.7$

Text Transcription:

x bar=317.2

s=15.7

ANSWER:

Step 1 of 2

Given,

Sample size, n = 10.

The mean,

The standard deviation,

Confidence Interval = 99%

We know that for and s, the mean and standard deviation of a random sample from a normal distribution with unknown variance , a Confidence Interval on is given by,

where is the upper percentage point of the t distribution with n – 1 degrees of freedom.

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