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Asked Dec 18, 2019
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13.12. Given large random samples from two binomial
populations, show that the null hypothesis 01 = 02 can
be tested on the basis of the statistic
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13.12. Given large random samples from two binomial populations, show that the null hypothesis 01 = 02 can be tested on the basis of the statistic

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X2
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.)
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X2 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.)

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Expert Answer

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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