Sampling Distributions: Proportions

Front

What is a sampling distribution?

Back

A sampling distribution is the probability distribution of a statistic (like a sample mean or proportion) obtained from a large number of samples drawn from a specific population.

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What is the Central Limit Theorem?

Back

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is sufficiently large, regardless of the population's distribution.

Front

What is the formula for the standard error of a proportion?

Back

The standard error (SE) of a proportion is calculated as SE = sqrt[p(1-p)/n], where p is the sample proportion and n is the sample size.

Front

What does 'n' represent in sampling distributions?

Back

'n' represents the sample size, which is the number of observations in a sample.

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What is the significance of np and nq in determining normality?

Back

For a sampling distribution to be approximately normal, both np (number of successes) and nq (number of failures) should be greater than 10.

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What is a Simple Random Sample (SRS)?

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A Simple Random Sample (SRS) is a sampling method where each member of the population has an equal chance of being selected.

Tags

CCSS.HSS.IC.B.3

Front

How does increasing sample size affect the shape of the sampling distribution?

Back

As the sample size increases, the sampling distribution becomes narrower and more closely approximates a normal distribution.

Tags

CCSS.6.SP.A.2

Front

What is the mean of a sampling distribution of sample proportions?

Back

The mean of a sampling distribution of sample proportions is equal to the population proportion (p).

Front

What is the relationship between sample size and standard error?

Back

As the sample size increases, the standard error decreases, indicating more precise estimates of the population parameter.

Front

What is the purpose of using a sampling distribution?

Back

Sampling distributions are used to make inferences about population parameters based on sample statistics.