Glossary

Z-Test

A Z-test is a statistical test used to determine the significance of differences between a sample mean and a population mean when the population standard deviation is known. It is named after the Z-distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. The Z-test is often used to test hypotheses, particularly in large sample sizes.

In a Z-test, the null hypothesis assumes that there is no significant difference between the sample mean and the population mean. The alternative hypothesis, on the other hand, suggests that there is a significant difference. By calculating the test statistic, which is the difference between the sample mean and the population mean divided by the standard deviation, we can determine the probability of observing such a difference under the null hypothesis.

To perform a Z-test, one needs to have a random sample from a population with a known standard deviation. The steps involved in a Z-test are as follows:

1. State the null and alternative hypotheses.
2. Set the desired level of significance (alpha).
3. Collect the sample data and calculate the sample mean.
4. Determine the critical value for the test statistic based on the level of significance.
5. Compute the test statistic using the formula: (sample mean - population mean) / (standard deviation / sqrt(sample size)).
6. Compare the test statistic to the critical value and make a decision: reject or fail to reject the null hypothesis.
7. Interpret the results and draw conclusions based on the decision.

The Z-test is widely used in various fields such as economics, psychology, and biology. It provides a method for researchers to determine whether the differences they observe are statistically significant or just due to random chance. By utilizing the Z-test, researchers can make more confident conclusions and decisions based on their data.

In conclusion, a Z-test is a powerful statistical tool used to determine the significance of differences between a sample mean and a population mean. By following the steps outlined above, researchers can make informed decisions based on their data and draw meaningful conclusions.

A wide array of use-cases

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