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For skewed distributions, a larger sample size is typically necessary for the Central Limit Theorem to hold. Sample sizes of over 30 are recommended, with some statisticians suggesting at least 50 or more due to the skewness.

Yes, the Central Limit Theorem can also be applied to sample proportions. When sampling for proportions, provided the sample size is large enough, the distribution of the sample proportion will be approximately normal.

The Central Limit Theorem justifies the use of the normal distribution to determine critical values and calculate p-values in hypothesis testing, even when the population distribution is unknown, provided the sample size is large enough.

As the sample size increases, the spread of the sampling distribution decreases (it becomes thinner), and its shape becomes more closely approximated to a normal distribution.

While there is no set rule for what makes a sample size 'sufficiently large,' it is commonly suggested that a sample size of 30 or more is enough for the Central Limit Theorem to be applicable.

The Central Limit Theorem (CLT) states that the sampling distribution of the sample mean will approximately be a normal distribution, regardless of the shape of the population distribution, provided the sample size is sufficiently large.

The Central Limit Theorem is significant because it can be applied to populations with any shape of distribution – whether normal, skewed, or otherwise. As the sample size increases, the sampling distribution of the mean will become increasingly normal.

The Central Limit Theorem is crucial because it allows for the use of normal probability distributions to make inferences about population means, even when the population distribution is not normal, as long as the sample size is large enough.

Primarily, the Central Limit Theorem applies to the distribution of sample means, but there are similar limit theorems for sums, and under certain conditions, for other statistics as well.