Brief : I'm from manufacturing industry, a processing machine in our production line used to do pressing, polishing and QA in one line. Now we have a new machine that will perform these separately at the same time. Ideally the new machine will be better than the old machine. I want to prove that average time taken by new machine is significantly less than old machine.
Null hypothesis - There is no significance difference
Alternate hypothesis - Time taken by new machine is less than old machine.
I initially planned on performing bootstrapping to identify the population distribution, assuming the data was normally distributed, I planned on Two sample t-test, else Mann Whitney U-test. There is also some extreme outliers like 2% in a data of 50K or more per hour because of machine malfunction. I thought of removing these outliers completely as they are less than 5%.
My problem is, during research I came across normality test ( Shapiro-Wilk) which I though might help to statistically confirm the normality. Then I ran into proportion tests for sample size, which is also being recommended. Then came across (winsorized mean), for replacing outliers with non-outliers.
With just a regular (trust me, am not over researching) research, I'm flooded with over information, which is quite confusing. What should be the ideal framework for my use case. What would you all recommend that I do, correct or refer???
I performed the all the steps I initially planned on performing But, now having second thoughts if that will be correct.