Question

A state wide water campaign was conducted to find out whether residents had reduced water consumption after the campaign. They were hoping that more than half of the households had indeed reduced their water consumption. They took a random sample of n​ = 10,000 residents of the state and found that​ 51% had reduced their water consumption. Although the difference between​ 50% and​ 51% is quite​ small, the effect was statistically significant. Which of the following is the best​ explanation? The proportion of 0.51 is large. There is a lot of variability in water usage from one person to another. The sample size is very​ large, so that even a small difference can be detected. The relative proportion is 0.51​ / 0.50​ = 1.02, which is greater than 1.

Answer 1

Sample size is very large.

Explanation:

The best explanation for the above situation is that the sample size is very large that a small difference is noticable.

For the sample size of 10000 51% proportion means 5100 people started saving water. While 50% proportion means 5000 people started saving water.

100 more people makes huge difference and contribution in saving water.