Use the statistic of Exercise 12 to rework Exercise 70, and verify that the square of the value obtained for z equals the value obtained for χ².

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

Exercise 70

In random samples, 46 of 400 tulip bulbs from one nursery failed to bloom and 18 of 200 tulip bulbs from another nursery failed to bloom. Use the χ² statistic to test the null hypothesis θ₁ = θ₂ against the alternative hypothesis θ₁  θ₂ at the 0.05 level of significance