Question

What is the main use of a one sample Z-Test? Please provide an example.

Answer 1

Solution:

One sample z-test is used to test whether population mean is significantly different from the hypothesized value or not. This test is used for large samples.

The test statistic used for one-sample z-test is given as follows:

Where, x̄ is sample mean, μ is the hypothesized value of population mean, σ is population standard deviation and n is sample size.

This test statistic follows normal distribution with mean 0 and standard deviation 1.

Example : Suppose it is claimed that average SAT score of a population is 1511 with standard deviation of 18 . We take a random sample of size 100 of SAT scores from this population and the sample mean of the SAT scores comes out to be 1515. Now if we want to test whether the population mean of SAT scores is equal to the claimed value of 1511 or not, then we can use one-sample z-test to test the claim.