A z-test result helps you determine if there's a significant difference between your sample data and a known population parameter. Here's how to interpret it:
1. Understand the Z-Score
The z-score represents the number of standard deviations your sample mean is away from the population mean. A higher absolute value of the z-score indicates a greater difference between your sample and the population.
2. Set Your Significance Level (Alpha)
The significance level (alpha) determines the threshold for rejecting the null hypothesis. A common alpha value is 0.05, meaning there's a 5% chance of rejecting the null hypothesis when it's actually true.
3. Calculate the P-Value
The p-value represents the probability of observing your sample data if the null hypothesis is true. A lower p-value indicates stronger evidence against the null hypothesis.
4. Compare P-Value to Alpha
- If p-value < alpha: Reject the null hypothesis. This means there's enough evidence to suggest a significant difference between your sample and the population.
- If p-value > alpha: Fail to reject the null hypothesis. This means there's not enough evidence to suggest a significant difference.
5. Interpret the Results
- Rejecting the null hypothesis: Your sample data provides evidence that the population parameter is different from the hypothesized value.
- Failing to reject the null hypothesis: Your sample data does not provide enough evidence to conclude that the population parameter is different from the hypothesized value.
Example
Suppose you want to test if the average height of students in a school is different from the national average of 5'7". You collect data from a sample of students and calculate a z-score of 2.5. Your alpha is set at 0.05.
- Z-score: 2.5 (indicates a significant difference from the population mean)
- P-value: 0.0124 (less than alpha)
- Conclusion: You would reject the null hypothesis, suggesting that the average height of students in this school is significantly different from the national average.
Remember, a z-test result only provides statistical evidence. It's important to consider the context and practical implications of your findings.
