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 => pnew material = pexisting material
Ha : Alternate Hypothesis => pnew material > pexisting 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.