Selecting a random sample is an example of a statistical experiment, and the sample statistic x is a numerical description of the result of the experiment. therefore, x is a random variable. the probability distribution of x is called the sampling distribution of x. in practice, you select one random sample and use the information from that sample to estimate the population parameter of interest. however, statisticians sometimes perform a procedure called repeated sampling, in which the experiment is run over and over again and the value of the sample statistic from each running of the experiment is recorded. the distribution of the sample statistics from the repeated sampling is an?
Question: Selecting a random sample is an example of a statistical experiment, and the sample statistic x is a numerical description of the result of the experiment. therefore, x is a random variable. the probability distribution of x is called the sampling distribution of x. in practice, you select one random sample and use the information from that sample to estimate the population parameter of interest. however, statisticians sometimes perform a procedure called repeated sampling, in which the experiment is run over and over again and the value of the sample statistic from each running of the experiment is recorded. the distribution of the sample statistics from the repeated sampling is an?
One of the most important concepts in statistics is the idea of a random variable. A random variable is a numerical outcome of a statistical experiment, such as selecting a random sample from a population. The random variable can take different values depending on the result of the experiment. For example, if we select a random sample of 10 students from a class and measure their heights, the average height of the sample is a random variable that can vary from sample to sample.
The set of all possible values that a random variable can take, along with their probabilities, is called the probability distribution of the random variable. For example, if we toss a fair coin, the random variable that represents the number of heads can take two values: 0 or 1, each with probability 0.5. The probability distribution of this random variable is a table that shows these values and probabilities.
Sometimes, we are interested in the probability distribution of a random variable that is based on another random variable. For example, suppose we want to estimate the mean height of all students in the class using the average height of the sample. The average height of the sample is a random variable that depends on the heights of the individual students in the sample, which are also random variables. The probability distribution of the average height of the sample is called the sampling distribution of the sample mean.
The sampling distribution of a sample statistic is very useful for making inferences about the population parameter that the statistic estimates. For example, we can use the sampling distribution of the sample mean to calculate confidence intervals and hypothesis tests for the population mean.
However, in practice, we usually do not know the sampling distribution of a sample statistic, because it would require us to know all possible samples and their statistics. Instead, we use one sample and its statistic to estimate the sampling distribution. This is where repeated sampling comes in.
Repeated sampling is a hypothetical procedure that involves running the same statistical experiment many times and recording the value of the sample statistic from each run. For example, if we select 10 students at random from the class and measure their heights, repeated sampling would mean doing this over and over again and recording the average height from each sample. The distribution of these averages is an approximation of the sampling distribution of the sample mean.
Repeated sampling is not something that we actually do in real life, because it would be too costly and time-consuming. However, it is a useful way to visualize and understand how sampling works and how different samples can lead to different estimates of the population parameter. Repeated sampling also helps us to assess how accurate and reliable our estimates are by showing us how much they can vary from run to run.
0 Komentar
Post a Comment