Which of the following best describes the sampling distribution of a statistic?Group of answer choicesA distribution of all parameters from the population that is to be randomly sampled.A normal curve, for which probabilities are obtained by standardizing.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.
Question
Which of the following best describes the sampling distribution of a statistic?Group of answer choicesA distribution of all parameters from the population that is to be randomly sampled.A normal curve, for which probabilities are obtained by standardizing.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.
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:
A sampling distribution is a probability distribution of a statistic obtained through a large number of samples drawn from a specific population. The sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of size n. It may be considered as the distribution of the statistic for all possible samples from the same population of a given size.
The other options do not accurately describe the sampling distribution of a statistic. For example, a distribution of all parameters from the population that is to be randomly sampled is not correct because parameters are fixed values about the population, not values that vary from sample to sample.
Similarly, a normal curve, for which probabilities are obtained by standardizing, is a description of a specific type of distribution (the normal distribution), not a description of a sampling distribution.
The mechanism that determines whether the random sampling was effective is more related to the process of sampling, not the distribution of the statistic itself.
Finally, a distribution of all possible summary statistics from a single random sample, from the same population, is not correct because a sampling distribution involves considering many possible samples, not just a single sample.
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?Group of answer choicesDistribution of summary statisticsRandom samplingDistribution of population parametersThe normal curveSampling distribution of a statistic
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
When the sampling distribution of a statistic centers exactly around the parameter it estimates we can say that the statistic is which of the following? Statistically significant Unbiased Equal to the parameter Normally distributed
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