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What assumption about the population should we be willing to make if a margin of error is desired?

a) The population is normal
b) The population is large
c) The population is small
d) The population is skewed

User EFenix
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1 Answer

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Final answer:

The assumption usually made if a margin of error is desired is that the population is normal or that the sample size is sufficiently large to invoke the Central Limit Theorem. The normality assumption is particularly important for small samples, while large samples help ensure the sampling distribution of the mean approximates normality.

Step-by-step explanation:

If a margin of error is desired, it is often assumed that the population is normal. This is because we rely on the Central Limit Theorem, which states that if the sample size (n) is sufficiently large (typically n >= 30), the distribution of the sample means will be approximately normal. This approximation holds true regardless of the population's distribution.

The assumption of normality is essential for small samples because many statistical tests are based on the normal distribution. However, when working with large samples, the normality assumption is less of a concern, and the key is a random and unbiased selection of a sufficiently large sample, typically n >= 30.

User Andre Haverdings
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