Z-Test

The z-test is a statistical test used to compare the means of two groups. It is a parametric test, which means that it assumes that the data is normally distributed. The z-test is used when the sample size is large (n > 30) and the population standard deviation is known.

The z-test is calculated by subtracting the mean of one group from the mean of the other group, and then dividing the result by the standard deviation of the combined groups. The resulting value is called the z-score.

The z-score is then compared to a critical value to determine whether the difference between the two means is statistically significant. The critical value is the value of z that has a probability of 0.05 of being exceeded by chance.

If the z-score is greater than the critical value, then the difference between the two means is statistically significant. If the z-score is less than the critical value, then the difference between the two means is not statistically significant.

The z-test is a powerful tool for comparing the means of two groups. However, it is important to note that the z-test only works when the data is normally distributed. If the data is not normally distributed, then the z-test may not be accurate.

Here is an example of how the z-test can be used to compare the means of two groups. Suppose we have two groups of students, one group that took a math class and one group that did not take a math class. We want to know if the students who took the math class had higher math scores than the students who did not take the math class.

We can use the z-test to compare the means of the two groups of students' math scores. We first need to calculate the mean and standard deviation of the math scores for each group. Then, we subtract the mean of the math scores for the group that did not take the math class from the mean of the math scores for the group that took the math class. We then divide the result by the standard deviation of the combined math scores.

The resulting z-score is 1.96. This z-score is greater than the critical value of 1.96, so we can conclude that the difference between the two means is statistically significant. This means that the students who took the math class had higher math scores than the students who did not take the math class.

The z-test is a powerful tool for comparing the means of two groups. However, it is important to note that the z-test only works when the data is normally distributed. If the data is not normally distributed, then the z-test may not be accurate.