Sampling Distributions Assessment

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What is the standard deviation of a sampling distribution?

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The standard deviation of a sampling distribution, also known as the standard error, is not the same as the standard deviation of the population. It is calculated as the population standard deviation divided by the square root of the sample size.

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What is a statistic in the context of sampling?

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A statistic is a numerical value that describes a characteristic of a sample. For example, in a survey where 43% of high school students say their mother taught them about managing money, 43% is a statistic.

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What is a parameter in statistics?

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A parameter is a numerical value that describes a characteristic of a population. It is a fixed value, unlike a statistic which can vary from sample to sample.

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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 will approach a normal distribution as the sample size increases, regardless of the shape of the population distribution.

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

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The standard deviation of the sampling distribution of sample means (standard error) is calculated using the formula: σ/√n, where σ is the population standard deviation and n is the sample size.

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What is the significance of a 75% recommendation rate in a sample of dentists?

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A 75% recommendation rate indicates that if a sample of dentists is surveyed, we can use this rate to assess the validity of claims made in advertisements, such as those for Trident gum.

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What does it mean if a sampling distribution is normally distributed?

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If a sampling distribution is normally distributed, it means that the sample means will cluster around the population mean, forming a bell-shaped curve.

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What is the difference between a sample and a population?

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A sample is a subset of individuals selected from a larger group (population) used to estimate characteristics of the whole population.

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What is the formula for calculating the standard error?

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The formula for calculating the standard error (SE) is SE = σ/√n, where σ is the population standard deviation and n is the sample size.

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What does a probability of .2846 indicate in a sampling context?

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A probability of .2846 indicates the likelihood that a certain outcome (e.g., percentage of dentists recommending a product) will occur within a specified range in a sampling distribution.