Statistics Final Exam

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What is a point estimate in statistics?

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A point estimate is a single value given as an estimate of a population parameter. For example, the proportion of 'yes' voters in a sample can be used as a point estimate for the proportion in the entire population.

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How do you calculate the proportion of 'yes' voters?

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The proportion of 'yes' voters is calculated by dividing the number of 'yes' votes by the total number of votes. For example, if there are 1757 'yes' votes out of 2584 total votes, the proportion is 1757/2584 = 0.6799535604.

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What is the significance of the mean in a normal distribution?

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The mean is the average value of a dataset and serves as the center of the normal distribution. In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.

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What does a standard deviation indicate in statistics?

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Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

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What is the z-score in statistics?

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

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What is the probability of selecting a value greater than a certain z-score in a normal distribution?

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The probability can be found using z-tables or normal distribution calculators, which provide the area under the curve to the left of the z-score. The area to the right gives the probability of selecting a value greater than that z-score.

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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 normally distributed, regardless of the shape of the population distribution, provided the sample size is sufficiently large (usually n > 30).

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How do you find the mean of the sampling distribution of p-hat?

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The mean of the sampling distribution of p-hat is equal to the true population proportion (p). For example, if the claim is that 40% of adults went to church, the mean of p-hat is 0.4.

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

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The probability of a sample mean can be calculated using the formula: P(X̄ < x) = P(Z < (x - μ) / (σ/√n)), where X̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

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What does it mean if a probability is expressed as a percentage?

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A probability expressed as a percentage indicates the likelihood of an event occurring, with 0% meaning it will not occur and 100% meaning it will certainly occur.