Does the sample size ? affect the standard deviation of all possible sample means? Explain your answer.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Does the
Sampling distribution of the sample mean:
- If the true population distribution of a random variable, say, x, is normal with parameters, mean μ and standard deviation σ, then, whatever be the size (n) of the sample taken from the population, the distribution of the sample mean is also normal, with parameters, mean μ and standard deviation .
- Even if the true population distribution of a random variable, say, x, is not normal and has population mean μ, standard deviation σ, then, for a large size (n ≥ 30) of a sample taken from the population, the distribution of the sample mean is approximately normal, with parameters, mean μ and standard deviation (by Central Limit Theorem).
- If the true population distribution of a random variable, say, x, is not normal and has population mean μ, standard deviation σ, then, for a small size (n< 30) of a sample taken from the population, the distribution of the sample mean cannot be said to be approximately normal.
Central Limit Theorem for mean:
If a random sample of size n is taken from a population having mean μ and standard deviation σ then, as the sample size increases, the sample mean approaches the normal distribution with mean and standard deviation .
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