Final answer:
The statement is true; as sample size increases, even small differences between two population proportions can lead to the rejection of the null hypothesis. The decreasing standard error with larger samples increases the test statistic, leading to smaller p-values. However, practical significance should also be considered alongside statistical significance.
Step-by-step explanation:
The statement regarding the hypothesis test for two population proportions is true. As the sample size increases, even a very small difference between the two population proportions becomes significant. This is because with larger sample sizes, the standard error of the difference between the two proportions decreases, which increases the test statistic used in hypothesis testing. As a result, we are more likely to reject the null hypothesis of equal population proportions if the sample size is sufficiently large, assuming there is indeed a small actual difference.
The null hypothesis typically states that there is no effect or no difference, and in the case of two population proportions, it states that the proportions are equal. When we conduct a hypothesis test, we calculate the probability of observing our sample data, or something more extreme, given that the null hypothesis is true. This probability is known as the p-value. A small p-value indicates that the observed data is unlikely under the null hypothesis, leading to its rejection.
However, it's important to note that the ability to detect small differences with large samples does not imply that those differences are practically significant, only statistically so. Therefore, in addition to hypothesis testing, it's essential to consider effect size and practical significance when interpreting results.