# 13.12. Given large random samples from two binomialpopulations, show that the null hypothesis 01 = 02 canbe tested on the basis of the statistic X2X1п2n1%3|ĝ(1 – Ô)null hypothn1 П2X1+x2where ê =(Hint: Refer to Exercise 8.5 on%3Dn +n2page 239.)

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1 views help_outlineImage Transcriptionclose13.12. Given large random samples from two binomial populations, show that the null hypothesis 01 = 02 can be tested on the basis of the statistic fullscreen help_outlineImage TranscriptioncloseX2 X1 п2 n1 %3| ĝ(1 – Ô) null hypoth n1 П2 X1+x2 where ê = (Hint: Refer to Exercise 8.5 on %3D n +n2 page 239.) fullscreen
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Step 1

Introduction:

[We have replaced the θ_hat symbol by p̂, simply due to typing convenience, and hence, also replaced each θ by p.]

Denote p1, p2 to be the true proportions of successes (or, proportions of cases with the characteristic of interest) of the two populations.

Suppose samples of sizes n1 and n2 are taken from the two respective populations.

Suppose x1 and x2 are the numbers of successes (or, numbers of cases with the characteristic of interest) observed in the samples from the first and second populations respectively.

Then, the sample proportions of the two populations are respectively 1 and 2, where 1 = x1/n1 and ...

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