STAT 5.5 sampling distribution

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What is a sampling distribution?

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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 the sample proportion?

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

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How do you calculate the standard deviation of the sampling distribution of the sample proportion?

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The standard deviation (σp̂) of the sampling distribution of the sample proportion is calculated using the formula: σp̂ = sqrt[(p(1-p))/n], where p is the population proportion and n is the sample size.

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

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As the sample size increases, the standard deviation of the sampling distribution decreases, leading to a more precise estimate of the population proportion.

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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 (or sample proportion) will be approximately normally distributed if the sample size is sufficiently large, regardless of the population's distribution.

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What is the relationship between sample size and the variability of sample proportions?

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Larger sample sizes result in less variability in sample proportions, leading to a tighter sampling distribution.

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What is the significance of a population proportion close to 1/2 in sampling distributions?

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A population proportion close to 1/2 maximizes the standard deviation of the sampling distribution, indicating the greatest variability in sample proportions.

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How do you interpret the mean of the sampling distribution?

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The mean of the sampling distribution represents the expected value of the sample proportion across all possible samples of a given size from the population.

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What is the formula for calculating the standard deviation of the sampling distribution when the population proportion is known?

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

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What does it mean if the sample proportion is significantly different from the population proportion?

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If the sample proportion is significantly different from the population proportion, it may indicate sampling error or that the sample is not representative of the population.