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Statistics / Probability and Statistical Inference 9 / Chapter 7.4 / Problem 15E

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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If to be a 90% confidence interval for ?X ??Y. Assume that

Chapter 7, Problem 15E

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QUESTION:

If \(\bar{X}\) and \(\bar{Y}\) are the respective means of two independent random samples of the same size \(n\), find \(n\) if we want \(\bar{x}-\bar{y} \pm 4\) to be a \(90 \%\) confidence interval for \(\mu_{X}-\mu_{Y}\). Assume that the standard deviations are known to be \(\sigma_{X}=15\) and \(\sigma_{Y}=25\).

Equation Transcription:

$\overline{X}$

$\overline{Y}$

$n$

$\overline{x}-\overline{y}±4$

$90\%$

${\mu{}}_{X}-{\mu{}}_{Y}$

${\sigma{}}_{X}=15$

${\sigma{}}_{Y}=25$

Text Transcription:

Bar X

bar Y

n

Bar x-bar y pm 4

90%

mu_X-mu_Y

sigma_ X=15

sigma_Y=25

Questions & Answers

QUESTION:

If \(\bar{X}\) and \(\bar{Y}\) are the respective means of two independent random samples of the same size \(n\), find \(n\) if we want \(\bar{x}-\bar{y} \pm 4\) to be a \(90 \%\) confidence interval for \(\mu_{X}-\mu_{Y}\). Assume that the standard deviations are known to be \(\sigma_{X}=15\) and \(\sigma_{Y}=25\).

Equation Transcription:

$\overline{X}$

$\overline{Y}$

$n$

$\overline{x}-\overline{y}±4$

$90\%$

${\mu{}}_{X}-{\mu{}}_{Y}$

${\sigma{}}_{X}=15$

${\sigma{}}_{Y}=25$

Text Transcription:

Bar X

bar Y

n

Bar x-bar y pm 4

90%

mu_X-mu_Y

sigma_ X=15

sigma_Y=25

ANSWER:

Step 1 of 3

Hence for Confidence interval

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