Given large random samples from two binomial populations, Basic Statistics

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Given large random samples from two binomial populations

Show that the square of the expression for z in Exercise 12 equals so that the two tests are actually equivalent when the alternative hypothesis is θ₁ θ₂. Note that the test described in Exercise 12, but not the one based on the χ² statistic, can be used when the alternative hypothesis is θ₁ ₂ or θ₁ > θ₂.

Exercise 12

Given large random samples from two binomial populations, show that the null hypothesis θ₁ = θ₂ can be tested on the basis of the statistic

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