The Z.TEST function in Google Sheets is a powerful statistical tool used to determine if a sample mean significantly differs from a known population mean. It is particularly useful in hypothesis testing, allowing users to evaluate the likelihood that an observed sample comes from a specific distribution.

Syntax

Z.TEST(data, x, [sigma])

• data: An array or range of observed values.
• x: The known population mean to compare against.
• sigma: (Optional) The known population standard deviation. If omitted, the function calculates it from the sample data.

Example #1

=Z.TEST(A1:A30, 100)

This function tests if the mean of the values in range A1:A30 significantly differs from 100. If the computed p-value is less than your alpha level (e.g., 0.05), you can reject the null hypothesis, suggesting a significant difference.

Example #2

=Z.TEST(A1:A30, 100, 15)

In this case, the function tests the mean of the values in A1:A30 against 100, assuming a population standard deviation of 15. The result will indicate the significance of the difference between the sample mean and the population mean with respect to the known standard deviation.

Example #3

=Z.TEST(A1:A30, A31)

This formula compares the sample mean from A1:A30 to a dynamic value present in cell A31. This offers flexibility in hypothesis testing as the population mean can be adjusted based on new information.

Error handling

• N/A: The function could not compute a result because the data set is empty or all data points are the same.
• DIV/0!: This error appears when the standard deviation is zero, which typically happens when the sample contains identical values.
• VALUE!: Indicates that the parameters provided cannot be evaluated, possibly due to incompatible data types.

Conclusion

The Z.TEST function in Google Sheets is invaluable for statistical analysis, particularly when conducting hypothesis tests regarding means. By understanding its syntax and application through various examples, users can effectively harness this tool to make informed decisions based on their data.