Question

using the central limit theorem, applied to the sampling distribution of the sample proportion, what conditions must be met?

Answer 1

Using the central limit theorem, the conditions are:

The population should be symmetrical. If the population is skewed sample size should be sufficiently large at least 30.

Samples should be drawn strictly at random.

The sample observations should be independent.

The central limit theorem states that, under certain circumstances, the sampling distribution of the sample mean is roughly normal.

The circumstances are

I) The population ought to be balanced. If the population is skewed, the sample size should be at least 30.

ii) Samples must be chosen completely at random.

iii) Independent observations for the sample should be used.

The sample size must be large (e.g., at least 30) as the necessary condition.

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