Enter the sample means, standard deviations, and sizes into the calculator to determine the Z score.

2 Sample Z Test Formula

The following formula is used to calculate the Z score in a 2 Sample Z Test.

Z = (X1 - X2) / sqrt((s1^2/n1) + (s2^2/n2))


  • Z is the Z score X1 and X2 are the sample means s1 and s2 are the standard deviations of the two samples n1 and n2 are the sizes of the two samples

To calculate the Z score, subtract the mean of the second sample from the mean of the first sample. Then, square the standard deviation of the first sample and divide it by the size of the first sample. Do the same for the second sample. Add these two results together and take the square root. Finally, divide the difference of the means by this result.

What is a 2 Sample Z Test?

A 2 Sample Z Test is a statistical method used to determine whether the difference between the means of two normally distributed populations is significant. It assumes that the populations have the same standard deviation and that the samples are independent of each other. The test calculates a Z-score, which represents the distance between the sample means in terms of standard deviations. This score is then compared to a critical value from the Z-distribution to determine if the difference between the means is statistically significant.

How to Calculate 2 Sample Z Test?

The following steps outline how to calculate a 2 Sample Z Test:

  1. First, determine the sample means (X1 and X2).
  2. Next, determine the standard deviations of the two samples (s1 and s2).
  3. Next, determine the sizes of the two samples (n1 and n2).
  4. Using the formula Z = (X1 – X2) / sqrt((s1^2/n1) + (s2^2/n2)), calculate the Z score.
  5. Finally, interpret the results of the Z test.

Example Problem:

Use the following variables as an example problem to test your knowledge:

X1 = 10

X2 = 8

s1 = 2

s2 = 3

n1 = 50

n2 = 60