If Y1/n and Y2/n are the respective independent relative

Chapter 7, Problem 14E

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QUESTION:

If \(Y_{1} / n\) and \(Y_{2} / n\) are the respective independent relative frequencies of success associated with the two binomial distributions \(b\left(n, p_{1}\right)\) and \(b\left(n, p_{2}\right)\), compute \(n\) such that the approximate probability that the random interval \(\left(Y_{1} / n-Y_{2} / n\right) \pm 0.05\) covers \(p_{1}-p_{2}\) is at least \(0.80\). Hint: Take \(p_{1}^{*}=p_{2}^{*}=1 / 2\) to provide an upper bound for \(n\).

Equation Transcription:

 

 

 

Text Transcription:

Y_1/n  

Y_2/n

b(n,p_1)  

b(n,p_2)

(Y_1/n-Y_2/n)pm0.05

p_1-p_2

 0.80

p-1^*=p_2^*=1/2

n

Questions & Answers

QUESTION:

If \(Y_{1} / n\) and \(Y_{2} / n\) are the respective independent relative frequencies of success associated with the two binomial distributions \(b\left(n, p_{1}\right)\) and \(b\left(n, p_{2}\right)\), compute \(n\) such that the approximate probability that the random interval \(\left(Y_{1} / n-Y_{2} / n\right) \pm 0.05\) covers \(p_{1}-p_{2}\) is at least \(0.80\). Hint: Take \(p_{1}^{*}=p_{2}^{*}=1 / 2\) to provide an upper bound for \(n\).

Equation Transcription:

 

 

 

Text Transcription:

Y_1/n  

Y_2/n

b(n,p_1)  

b(n,p_2)

(Y_1/n-Y_2/n)pm0.05

p_1-p_2

 0.80

p-1^*=p_2^*=1/2

n

ANSWER:

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