Final answer:
The Excel function to perform a one-sample z-test is Z.TEST, used to determine if there's a significant difference between a sample mean and a population mean when the population standard deviation is known.
Step-by-step explanation:
The Excel function for performing a one-sample z-test is Z.TEST. When you perform a hypothesis test of a single population mean μ using a normal distribution, you are conducting a z-test. This test is appropriate when the population you are testing is normally distributed, or when the sample size is sufficiently large. Moreover, for a z-test, you must know the value of the population standard deviation, which is rarely known in reality.
A z-score is a standardized value used in this process. The mean of the z-scores is zero, and the standard deviation is one. The formula for z-score is z = (x - μ) / σ, which gives the number of standard deviations a sample mean x is from the population mean μ. The Z.TEST function in Excel calculates the p-value by performing a normal probability calculation, which is essential in determining whether to reject the null hypothesis.