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Asked Dec 18, 2019

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**Introduction:**

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

Denote *p*1, *p*2 to be the true proportions of successes (or, proportions of cases with the characteristic of interest) of the two populations.

Suppose samples of sizes *n*1 and *n*2 are taken from the two respective populations.

Suppose *x*1 and *x*2 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 *p̂*1 and *p̂*2, where *p̂*1 = *x*1/*n*1 and *...*

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