Z- Test

A Z-test is a hypothesis test based on the Z-statistic, which follows the standard normal distribution under the null hypothesis. Z-test is used if

 

• Sample size is greater than 30.

• Data points are independent of each other, i.e. one data point is not related or does not affect another data point.

• Data is randomly selected from a population, where each item has an equal chance of being selected.

 

 

Test statistic/ Z-test = (sample statistic) - (value of parameter according to null hypothesis)

                (Standard error of sample statistic)

 

Example

Consider the size (diameter) of a ball to be 30 cm in a production process. A sample of 400 balls is taken and the mean diameter is found to be 28 cm with a standard deviation of 2 cm. With a 95% confidence interval, find out whether the production process is efficient.

 

Hypothesis:

H0: Mean diameter of the population = 30

H1: Mean diameter of the population   30

 

Test statistic

Z statistic = (28-30)/2 = -1

 

P value

P(z>=-1) = 0.1586 >= 0.05 (for 95% confidence interval)

 

Interpretation

Hence, null hypothesis cannot be rejected and so, production process is correct.