Which of the following best describes the sampling distribution of a statistic? A distribution of all parameters from the population that is to be randomly sampled. The mechanism that determines whether the random sampling was effective. A distribution of all possible summary statistics from a single random sample, from the same population. A distribution of a single statistic from repeated random samples of the same size, from the same population. A normal curve, for which probabilities are obtained by standardizing.
Question
Which of the following best describes the sampling distribution of a statistic? A distribution of all parameters from the population that is to be randomly sampled. The mechanism that determines whether the random sampling was effective. A distribution of all possible summary statistics from a single random sample, from the same population. A distribution of a single statistic from repeated random samples of the same size, from the same population. A normal curve, for which probabilities are obtained by standardizing.
Solution
The best description for the sampling distribution of a statistic is: "A distribution of a single statistic from repeated random samples of the same size, from the same population."
Here's why:
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"A distribution of all parameters from the population that is to be randomly sampled." - This is not correct because the sampling distribution is not about the distribution of all parameters from the population, but about the distribution of a statistic based on samples.
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"The mechanism that determines whether the random sampling was effective." - This is not correct because the sampling distribution is not a mechanism, but a concept in statistics.
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"A distribution of all possible summary statistics from a single random sample, from the same population." - This is not correct because the sampling distribution is not about all possible summary statistics from a single sample, but about a single statistic from multiple samples.
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"A distribution of a single statistic from repeated random samples of the same size, from the same population." - This is the correct answer. The sampling distribution is about how a statistic behaves when we take many random samples of the same size from the same population.
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"A normal curve, for which probabilities are obtained by standardizing." - This is not correct because not all sampling distributions are normal. The shape of the sampling distribution depends on the statistic and the distribution of the population.
Similar Questions
A distribution of a single statistic from repeated random samples of the same size from the same population refers to which of the following? Distribution of summary statistics The normal curve Distribution of population parameters Sampling distribution of a statistic Random sampling
In statistics, a sampling distribution refers to:A.A) The process of selecting a representative sample from a population. B. B) The distribution of sample statistics (e.g., sample means) obtained from multiple samples of the same size from a population. C.C) The distribution of the entire population. D.D) The distribution of outliers in a dataset.
Which of the following statements best describes the relationship between a parameter and a statistic?Question 17Select one:a.A parameter has a sampling distribution with the statistic as its mean.b.A parameter has a sampling distribution used to determine values a statistic may have in repeated samples.c.A statistic is used to estimate a parameter.d.A parameter is used to estimate a statistic.
What can one say about the sampling distribution of a sample statistic based on a simple random sample?Group of answer choicesIt is about bell-shaped and peaks above the parameterIt is usually skewed if the population concerns incomesIt will be roughly a straight lineNothing can be said in advance about the sampling distribution since the sampling was random
The sampling distribution of the sample proportion is the distribution of values of the sample proportion from all possible samples of size n drawn from a population. When a sample proportion is calculated, the population from which the sample comes is discrete. The variance of the sample proportion is equal to the variance of a binomial random variable divided by the sample size squared. The sampling distribution of the sample proportion is approximately normally distributed provided the population is normally distributed.
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