Following is a case study related to the application of 2-proportion test.

*Currently, there were 5 production lines running the same product. All the 5 production lines were using the same version of machines. A process engineer would like to assess if changes on raw material would improve the Yield(%) significantly. He ran 1 production line with new raw material for 7 days with Yield measured as 97.8% ( Total:1250, Pass:1222 ) as compared to 96.8% ( Total:1250, Pass:1210 ) using current raw material.*

So, the **practical question** here was “Was the new raw material improve the Yield significantly?”

It was then translated to **statistical question** by means of Hypothesis Statement.

Ho : Null Hypothesis => p

_{new material }= p_{existing material}Ha : Alternate Hypothesis => p

_{new material }> p_{existing material}

Next, conduct **Statistical Analysis**. In Minitab, click **Stat>Basic Statistics>2-proportion **and fill up relevant information. Then, click **Options** and select the right field below.

Click **OK** and **OK** to view the analysis result from Minitab Session window below.

**Test and CI for Two Proportions**

Sample X N Sample p

1 1222 1250 0.977600

2 1210 1250 0.968000

Difference = p (1) – p (2)

Estimate for difference: 0.0096

95% lower bound for difference: -0.00109780

Test for difference = 0 (vs > 0): Z = 1.48 P-Value = 0.070

Fisher’s exact test: P-Value = 0.088

The Pvalue was 0.070. Fail to reject Ho (assuming Alpha risk of 5% i.e. 0.05 )

**Statistically**, it was to say No significant difference between Yield% using new and existing raw materials.

**Practically**, it was concluded that there was no evidence to show new raw material would improve the Yield significantly.