STAT 5.5 sampling distribution

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What is a sampling distribution?

Back

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

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What is the mean of a sampling distribution?

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The mean of a sampling distribution is equal to the mean of the population from which the samples are drawn.

Tags

CCSS.6.SP.A.2

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What happens to the variability of the sampling distribution as the sample size increases?

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As the sample size increases, the variability (or standard deviation) of the sampling distribution decreases.

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What is the standard error of the sample proportion?

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

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What is the Central Limit Theorem?

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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.

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How does sampling with replacement differ from sampling without replacement?

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In sampling with replacement, each member of the population can be selected more than once, while in sampling without replacement, once a member is selected, it cannot be chosen again.

Tags

CCSS.HSS.IC.B.3

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What is the effect of reducing sample size on the variance of the sampling distribution?

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Reducing the sample size increases the variance of the sampling distribution.

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What is a sample proportion?

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A sample proportion is the ratio of the number of successes in a sample to the total number of observations in that sample.

Tags

CCSS.HSS.IC.B.4

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What is the formula for calculating the standard deviation of the sampling distribution of a sample proportion?

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The formula is sqrt[(p(1-p)/n)], where p is the sample proportion and n is the sample size.

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What does it mean if a sampling distribution is skewed?

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If a sampling distribution is skewed, it means that the distribution is not symmetrical and has a longer tail on one side than the other.