Dec 13th Pack Day Assignment

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What is a z-score?

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A z-score indicates how many standard deviations an element is from the mean. It is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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How do you calculate the z-score for a given value?

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To calculate the z-score, subtract the mean from the value and then divide by the standard deviation: z = (X - μ) / σ.

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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.

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What does the standard deviation of a sampling distribution represent?

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The standard deviation of a sampling distribution, also known as the standard error, measures the dispersion of sample means around the population mean.

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What is the Central Limit Theorem?

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The Central Limit Theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

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What is the formula for the standard error of the mean?

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The standard error of the mean (SEM) is calculated as SEM = σ / √n, where σ is the population standard deviation and n is the sample size.

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What does phat represent in statistics?

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Phat (p̂) represents the sample proportion, which is the number of successes in a sample divided by the total number of observations in that sample.

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What is the significance of a negative z-score?

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A negative z-score indicates that the value is below the mean of the distribution.

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What is the significance of a positive z-score?

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A positive z-score indicates that the value is above the mean of the distribution.

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How do you interpret a z-score of 1.14?

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A z-score of 1.14 means that the value is 1.14 standard deviations above the mean.