Sampling Distributions: Proportions

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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 the sampling distribution of sample proportions?

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

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What is the standard error of the sample proportion?

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The standard error of the sample proportion (SE) is calculated as SE = 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 distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

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What does 'n' represent in sampling?

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In sampling, 'n' represents the sample size, or the number of observations in the sample.

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What is the significance of the sample size in relation to the sampling distribution?

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As the sample size increases, the sampling distribution becomes narrower and approaches a normal distribution, leading to more accurate estimates of the population parameter.

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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.

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What is the relationship between sample size and the shape of the sampling distribution?

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As the sample size increases, the shape of the sampling distribution becomes more normal, regardless of the shape of the population distribution.

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What is the formula for calculating the probability of a sample proportion?

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The probability of a sample proportion can be calculated using the normal approximation to the binomial distribution when np and n(1-p) are both greater than 5.

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What does 'phat' represent?

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'phat' represents the sample proportion, which is the number of successes in the sample divided by the sample size.