What Z-statistic is
A Z-statistic is a standardized measure of a statistic based on the standard normal distribution. It is used to compare a statistic to the standard normal distribution and to determine the significance of a sample statistic.
Steps for calculating a Z-statistic include:
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Calculate the sample mean (x̄) and sample standard deviation (s).
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Calculate the standard error (SE) of the sample using SE = s/√n, where n is the sample size.
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Calculate the Z-score (Z) by subtracting the population mean (μ) from the sample mean (x̄) and dividing by the standard error (SE): Z = (x̄−μ)/SE.
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Compare the Z-score to the standard normal distribution to determine the significance of the sample statistic.
Examples
- Computing the probability that two population means are equal by comparing their z-scores.
- Testing the difference between two proportions by comparing their z-scores.
- Performing a hypothesis test to compare the means of two independent samples.
- Estimating the differences between two population proportions.
- Determining if two samples have the same variance.