Tom was driving a Key Six Sigma Project for his company. He had done all the hardwork and reduced the Average Handle Time of this Process by almost 20%.

For an old process the mean TAT was 3.5 days to resolve JIRA tickets and the standard deviation was 0.65{data collected for a quarter with more than 30 data points, standard deviation was calculated using stddev.s in excel} .

The Project Team initiated some improvement actions to reduce the turn around time.

This current quarter’s sample data shows the mean turn around time to resolve high priority tickets as 2.75 days. The sample size is 50.

The task now was to prove that improvement had indeed been achieved!!!

In other words the task now is to verify with 95% confidence level, whether the mean turn around time to resolve high priority tickets has indeed been reduced. { Prove that your efforts have worked to improve the process}

This is where Tom looked at the Master Black Belt for guidance. #

### The MBB(Master Black Belt) instructed Tom to study about one sample Z test and meet him once he was ready. #1Approach to Closing that AHT Project

The one-sample z-test is used to test whether the mean of a population is greater than, less than, or not equal to a specific value. Because the standard normal distribution is used to calculate critical values for the test, this test is often called the one-sample z-test. The z-test assumes that the population standard deviation is known.

How to Run a One Sample Z Test

A one sample z test is one of the most basic types of hypothesis test. In order to run a one sample z test, you work through several steps:

Step 1: State the Null Hypothesis. This is one of the common stumbling blocks–in order to make sense of your sample and have the one sample z test give you the right information you must make sure you’ve written the null hypothesis and alternate hypothesis correctly.

Step 2: Use the z-formula to find a z-score.

All you do is put in the values you are given into the formula. Your question should give you the sample mean (x̄), the standard deviation (σ), and the number of items in the sample (n). Your hypothesized mean (in other words, the mean you are testing the hypothesis for, or your null hypothesis) is μ0.

In the above example:

Hypothesized population mean (µ0) : 3.5

Sample Mean (X bar) 2.75

Standard deviation (of population or sample) 0.65

Sample size (n) 50

Confidence level % 95

Use one sample Z test calculator template with these values to do the hypothesis test

Null Hypothesis Mu = 3.5

We have to prove that the mean turn around time is reduced?

Hence it is a Left Tailed Test

Alternate Hypothesis Mu<3.5

Z Computed value should be greater than Z critical Value for Null Hypothesis to be true

Please see attached file for complete solution.

Statisticshowto.com explains Z tests that help Project Managers and Quality Managers alike