as the sample size increases, the distribution of the sample proportion becomes more normal. this fact is due to

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09-12-2022
Mathematics

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as the sample size increases, the distribution of the sample proportion becomes more normal. this fact is due to

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-16T08:18:30-05:00

the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal.

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal. This means that the mean of the sample will be closer to the mean of the population, and the variability of the sample will be smaller. Since the sample proportion is just the mean of the sample, as the sample size increases, the distribution of the sample proportion will also become more normal. The larger the sample size, the more likely it is that the sample will accurately represent the population, and the more normal the distribution of the sample proportion will be. In other words, the sample proportion will be closer to the true population proportion, and the variability of the sample proportion will be smaller.

Learn more about central limit theorem here

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