Provide explanation with correct answer to this question please. A state wide wa

Question

Provide explanation with correct answer to this question please.

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 o the state and ound that 519 had reduced ther water consumption. Althou g the difference between 50% and 51% s quite sma the effect as statistically si ica hi o the following is the best explanation? OA. O B. The proportion of 0.51 is large. There is a lot of variability in water usage from one person to another. C. 0 D. The relative proportion is 0.51 / 0.50-102, which is greater than 1. The sample size is very large, so that even a small difference can be detected.

Explanation / Answer

When the sample size is very large, the effect is also bigger.

In the example, the difference is 0.51 - 0.50 = 0.01

The percentage difference is 0.01 / 0.50 = 0.02 which should have been statistically insignificant as it is less than 0.05.

However, due to the large sample size even a difference of 0.02 can be detected.

So the answer is D.

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