Question

In: Statistics and Probability

A sampling distribution refers to the distribution of:

A sampling distribution refers to the distribution of:

  • repeated populations
  • repeated samples
  • a sample statistic
  • a population parameter

Solutions

Expert Solution

Concepts and reason

The concepts of population, repeated samples, sample statistic, population parameter, and sampling distribution are used to solve this problem.

The population is the total set of observations that can be collected for the variable under study. A population parameter is a numerical quantity that symbolizes a specific population.

A sample is a subset of the population. In repeated samples, the same subjects are tested under different conditions.

A sample statistic is a quantity that is derived from the sample drawn from the population. This quantity is used to estimate some of the unknown quantities of the population.

Sampling distribution can be defined as the probability distribution of the statistic defined based on the random sample selected from a large population. The sampling distribution of the statistic is defined along with its mean and variance.

Fundamentals

The population is a set of items or events of the variable of interest. Repeated populations are used to perform population analysis. It is a set of all the possible values.

Population parameter represents the population's characteristics, representing the entire population like population mean, population standard deviation, and population proportion.

The sample statistic is a quantity that is computed using the sample drawn from a population like a sample means, sample standard deviation, etcetera.

The sampling distribution is a function that associates probabilities with various values of a random variable, X.

 

The first option, “repeated populations,” is incorrect because a sampling distribution is defined for a random variable and used to perform population analysis.

The second option, “repeated samples,” is incorrect because a sampling distribution is not related to the repeated samples.

The fourth option, “population parameter,” is incorrect because the population's parameters characterize the entire population.

If numerous samples are drawn from an entire population, and for each sample, a certain sample statistic is calculated, then the distribution of these sample statistics is known as the sampling distribution. Hence, the third option can be considered as the correct answer choice.

Ans:

A sampling distribution refers to the distribution of a sample statistic.

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