In the previous blogs Hypothesis Testing ( Part 1 – 8 ), the statistical tools covered were related to “mean(m)” and “Variance(σ/σ2)”. In this blog onward, “Proportion(p)” will be discussed.
Basically, proportion data is derived from the ratio of binary data. E.g. of binary data are Yes/No, Pass/Fail, Go/No Go and etc. The ratio can be expressed as %.
Following is a case study related to the application of 1-proportion test.
A process engineer had set up a new production line due to expansion program. The new production line (equipped with newer version of machine) would produce the same product as in other older production lines. Historically, the average Yield(%) measured in older production lines was 95.8%. The process engineer would like to know if the Yield (%) of new production line was significantly better than older production lines. The new production line was run for 7 days and the Yield(%) was 96.2% ( total:1250, Pass:1203)
So, the practical question here was “Was the new production line Yield better than old production lines?”
It was then translated to statistical question by means of Hypothesis Statement.
Ho : Null Hypothesis => pnew = 95.8%
Ha : Alternate Hypothesis => pnew > 95.8%
Next, conduct Statistical Analysis. In Minitab, click Stat>Basic Statistics>1-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 One Proportion
Test of p = 0.958 vs p > 0.958
95% Lower Exact
Sample X N Sample p Bound P-Value
1 1203 1250 0.962400 0.952301 0.244
The Pvalue was 0.244. Fail to reject Ho (assuming Alpha risk of 5% i.e. 0.05 )
Statistically, it was to say No significant difference between Yield% of new and old production lines.
Practically, it was concluded Yield% of new production line was NOT better than old production lines.