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Why is the central limit theorem an important idea for dealing with a population not normally distributed?
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
Describe the central limit theorem and give an example of how it can be used in statistics?
The Central Limit Theorem (CLT) is a theorem that describes the fact that if a number of samples are taken from a population, the distribution of the means of the samples will be normal. This is true for all different distributions, whether or not the population is normal or something else. The main exception to this is that the theorem does not work particularly well if the samples are small (
Will the sampling distribution of the mean always be approximatelly normally distributed?
Yes, and more so for larger samples. (It follows from the Central Limit Theorem.)
Will sample means be nearly normally distributed if the distribution of the measurement among the individuals are not from a normal distribution?
Yes, as you keep drawing more and more samples and the number of samples become sufficiently large. This is known as the Central Limit Theorem.
When is the sample mean over repeated samples from the same population or process not normally distributed?
Provided the samples are independent, the Central Limit Theorem will ensure that the sample means will be distributed approximately normally with mean equal to the population mean.
Why is the central limit theorem an important idea for dealing with a population not normally distributed?
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
The Central Limit Theorem is important in statistics because?
According to the central limit theorem, as the sample size gets larger, the sampling distribution becomes closer to the Gaussian (Normal) regardless of the distribution of the original population. Equivalently, the sampling distribution of the means of a number of samples also becomes closer to the Gaussian distribution. This is the justification for using the Gaussian distribution for statistical procedures such as estimation and hypothesis testing.
The Central Limit Theorem defines large samples as having at least 36 elements?
False
What role does the Central Limit Theorem play in evaluation of the confidence level or hypothesis testing?
Without getting into the mathematical details, the Central Limit Theorem states that if you take a lot of samples from a certain probability distribution, the distribution of their sum (and therefore their mean) will be approximately normal, even if the original distribution was not normal. Furthermore, it gives you the standard deviation of the mean distribution: it's σn1/2. When testing a statistical hypothesis or calculating a confidence interval, we generally take the mean of a certain number of samples from a population, and assume that this mean is a value from a normal distribution. The Central Limit Theorem tells us that this assumption is approximately correct, for large samples, and tells us the standard deviation to use.
Describe the central limit theorem and give an example of how it can be used in statistics?
The Central Limit Theorem (CLT) is a theorem that describes the fact that if a number of samples are taken from a population, the distribution of the means of the samples will be normal. This is true for all different distributions, whether or not the population is normal or something else. The main exception to this is that the theorem does not work particularly well if the samples are small (
Will the sampling distribution of the mean always be approximatelly normally distributed?
Yes, and more so for larger samples. (It follows from the Central Limit Theorem.)
How can you compare means of two samples when the samples are chi square distributed?
According to the Central Limit Theorem if the sample size is large enough then the means will tend towards a normal distribution regardless of the distribution of the actual sample.
When is the sample mean over repeated samples from the same population or process not normally distributed?
Provided the samples are independent, the Central Limit Theorem will ensure that the sample means will be distributed approximately normally with mean equal to the population mean.
Will sample means be nearly normally distributed if the distribution of the measurement among the individuals are not from a normal distribution?
Yes, as you keep drawing more and more samples and the number of samples become sufficiently large. This is known as the Central Limit Theorem.
Why is central limit theorem important?
The central limit theorem is one of two fundamental theories of probability. It's very important because its the reason a great number of statistical procedures work. The theorem states the distribution of an average has the tendency to be normal, even when it turns out that the distribution from which the average is calculated is definitely non-normal.
Explain how you could create a distribution of means by taking a large number of samples of four individuals each?
As the sample size increases, and the number of samples taken increases, the distribution of the means will tend to a normal distribution. This is the Central Limit Theorem (CLT). Try out the applet and you will have a better understanding of the CLT.
What does the central limit theorem say about the shape of the sampling distribution of?
The central limit theorem can be used to determine the shape of a sampling distribution in which of the following scenarios?
