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 does the mean of a sampling distribution represent?

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The mean of a sampling distribution represents the average of all possible sample means or sample proportions from a population, and it is equal to the population parameter.

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What is the standard deviation of a sampling distribution called?

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The standard deviation of a sampling distribution is called the standard error.

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How do you calculate the standard error of the sample proportion?

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The standard error of the sample proportion (p̂) is calculated using the formula: 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 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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What is the relationship between sample size and variability in sampling distributions?

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As the sample size increases, the variability (or spread) of the sampling distribution decreases, leading to a more accurate estimate of the population parameter.

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What does it mean if a sampling distribution is approximately normal?

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If a sampling distribution is approximately normal, it means that the distribution of sample means or proportions follows a bell-shaped curve, allowing for the use of normal probability methods.

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What is the significance of a sample proportion of 0.11 in a sampling distribution?

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A sample proportion of 0.11 indicates that, on average, 11% of the sampled population exhibits the characteristic of interest (e.g., being late to work) in repeated samples.

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How does the sample size affect the likelihood of observing extreme sample proportions?

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Smaller sample sizes tend to have more variability, making it more likely to observe extreme sample proportions compared to larger sample sizes, which are more stable.

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What is the formula for the mean of the sampling distribution of the sample proportion?

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