A pollster is interested in comparing the proportions of women and men in a particular town who are in favor of a ban on fireworks within town borders. The pollster plans to test the hypothesis that the proportion of women in favor of the ban is diﬀerent from the proportion of men in favor of the ban. There are 4,673 women and 4,502 men who live in the town. From a simple random sample of 40 women in the town, the pollster finds that 38 favor the ban. From an independent simple random sample of 50 men in the town, the pollster finds that 27 favor the ban. Which of the following statements is true about this situation?

(A) Because the samples are from normal populations, a two-proportion z-test would be valid.

(B) Because the size of each sample is greater than 30, a two-proportion z-test would be valid.

(C) Because the number who favored the ban is greater than 10 in both groups, a two-proportion z-test would be valid

(D) Because of the relative sizes of the populations and samples, a two-proportion z-test would be valid.

(E) A two-proportion z-test would not be valid for these data.

Z test is a type of a statistical test for which the distribution of the data, the distribution of the test statistic under the null hypothesis is made with the help of the and under the normal distribution.

The purpose and the aim of the Z test is to test mean of the distribution of the data but the condition of applying a Z test in the sample is that the variance of the population should be known. Without knowing the variance of the population, we can not apply it.