1. What is a Critical Z Value?

The critical Z value represents how many standard deviations a data point (X) is from the mean (μ) in a normal distribution. It's a dimensionless quantity used in hypothesis testing and confidence interval estimation.

2. How Does the Calculator Work?

The calculator uses the Z-score formula:

Where:

• \( X \) — The raw score/data point
• \( \mu \) — The mean of the population
• \( \sigma \) — The standard deviation of the population

Explanation: The formula standardizes any normal distribution, allowing comparison across different scales and measurements.

3. Importance of Z Value Calculation

Details: Z-scores are fundamental in statistics for determining probabilities, identifying outliers, and making inferences about population parameters.

4. Using the Calculator

Tips: Enter the X value, population mean (μ), and population standard deviation (σ). Standard deviation must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a Z-score of 0 mean?
A: A Z-score of 0 means the data point is exactly at the mean of the distribution.

Q2: What is considered a significant Z-score?
A: Typically, Z-scores beyond ±1.96 are considered significant at the 95% confidence level (p < 0.05).

Q3: Can Z-scores be negative?
A: Yes, negative Z-scores indicate values below the mean, while positive scores indicate values above the mean.

Q4: How is this different from a t-score?
A: Z-scores are used when population parameters are known, while t-scores are used with sample statistics.

Q5: What's the relationship between Z-scores and p-values?
A: Z-scores can be converted to p-values using the standard normal distribution table or function.