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.

Related Solutions

Why is sampling distribution a theoretical distribution?
Why is sampling distribution a theoretical distribution?
1. What is a Sampling Distribution? 2. How is a Sampling Distribution created? 3. Explain the...
1. What is a Sampling Distribution? 2. How is a Sampling Distribution created? 3. Explain the Central Limit Theorem in terms of having a normal Sampling Distribution. 4. Why is having a normal Sampling Distribution important? 5. How do we calculate the mean for a Sampling Distribution? 6. How do we calculate the standard deviation for a Sampling Distribution? 7. How is the mean and standard deviation for a Sampling Distribution affected as the sample size increases? 8. How do...
Define sampling distribution. b. Explain why the spread (variance) of a sampling distribution for estimating a...
Define sampling distribution. b. Explain why the spread (variance) of a sampling distribution for estimating a mean would be smaller than the spread (variance) of the whole population. c. Discuss what happens to the shape AND spread of a sampling distribution as sample size (n) is increased. d.Explain why it is essential that the sampling distribution be normally distributed (or t-distributed) in order to do the statistical inference procedures we use in Chapters 9, 10 and 11.
What does “distribution sampling” reveal to the researcher. Give an example of how “distribution sampling” is...
What does “distribution sampling” reveal to the researcher. Give an example of how “distribution sampling” is used in a real-world scenario. Write a one to two (1–2) page short paper in which you answer the questions about distribution sampling.
Explain how a sampling distribution is created. What does the mean (center) of the sampling distribution...
Explain how a sampling distribution is created. What does the mean (center) of the sampling distribution tell us? What is the standard deviation of the sampling distribution called and what does it tell us? Explain the central limit theorem. Why is it important for a sampling distribution of sample means and sample proportions to be normal? What requirement ensures that a sampling distribution for sample means is normal? What requirement ensures that a sampling distribution for sample proportion is normal?...
What does “distribution sampling” reveal to the researcher. Give an example of how “distribution sampling” is...
What does “distribution sampling” reveal to the researcher. Give an example of how “distribution sampling” is used in a real-world scenario. Write a one to two (1–2) page short paper in which you answer the questions about distribution sampling
the functional distribution of income refers to distribution of income between
the functional distribution of income refers to distribution of income between
Generating the sampling distribution of M
Generating the sampling distribution of M Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, 7,8, 9, and 10 by drawing samples from these values, calculating the mean of each sample, and then considering the sampling distribution of the mean. To do this, suppose you perform an experiment in which you roll a ten-sided die two times (or equivalently, roll two ten-sided dice one time) and calculate the mean of your sample. Remember that your population is...
Generating the sampling distribution of M
Generating the sampling distribution of M Let's examine the mean of the numbers 1, 2, 3, 4, 5, 6, 7,8, 9, and 10 by drawing samples from these values, calculating the mean of each sample, and then considering the sampling distribution of the mean. To do this, suppose you perform an experiment in which you roll a ten-sided die two times (or equivalently, roll two ten-sided dice one time) and calculate the mean of your sample. Remember that your population is...
What is the sampling distribution of a statistic
What is the sampling distribution of a statistic
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT