A population has a standard deviation of σ = 18. On average, how much difference should exist between the population mean and the sample mean for n = 4 scores randomly selected from the population?
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.
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A sample of n = 4 scores has a mean of M = 75. Find the z-score for this sample:
a. If it was obtained from a population with μ = 80 and σ = 10.
b. If it was obtained from a population with μ = 80 and σ = 20.
c. If it was obtained from a population with μ = 80 and σ = 40.
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