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Give the statement of the Central Limit Theory and explain its significance inInferential
statistics ?
Charity Marange
Dec 13, 2023
Give the statement of the Central Limit Theory and explain its significance inInferential statistics ?
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ChatGPT
Dec 13, 2023
The Central Limit Theorem (CLT) states that the sampling distribution of the mean of any independent, random variable will tend to be approximately normally distributed, regardless of the shape of the original population, as the sample size increases.
The significance of the Central Limit Theorem in inferential statistics is that it allows us to make inferences about a population based on a sample. It provides a foundation for many statistical techniques and hypothesis testing.
The CLT allows us to assume that the sampling distribution of the mean will be normally distributed, even if the population distribution is not. This is important because the normal distribution is well understood and has many useful properties. It allows us to calculate probabilities and make statistical inferences using techniques such as confidence intervals and hypothesis tests.
Additionally, the CLT allows us to estimate population parameters, such as the population mean, by using the sample mean. This is particularly useful when it is not feasible or practical to collect data from an entire population.
Overall, the Central Limit Theorem is a fundamental concept in inferential statistics as it provides a basis for making statistical inferences and estimating population parameters based on sample data.
The significance of the Central Limit Theorem in inferential statistics is that it allows us to make inferences about a population based on a sample. It provides a foundation for many statistical techniques and hypothesis testing.
The CLT allows us to assume that the sampling distribution of the mean will be normally distributed, even if the population distribution is not. This is important because the normal distribution is well understood and has many useful properties. It allows us to calculate probabilities and make statistical inferences using techniques such as confidence intervals and hypothesis tests.
Additionally, the CLT allows us to estimate population parameters, such as the population mean, by using the sample mean. This is particularly useful when it is not feasible or practical to collect data from an entire population.
Overall, the Central Limit Theorem is a fundamental concept in inferential statistics as it provides a basis for making statistical inferences and estimating population parameters based on sample data.
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