Hypothesis testing for 2 sample proportion

[underwood]

Previously, the manager measured that the machine effectiveness was at 67.3% with a sample of size of 9. The team has made some improvements by reducing the time of changeovers, major stops and speed loss. Since those improvements, the manager has measured a rate of effectiveness at 78.2% with a sample size of 12. The goal was to increase effectiveness by 10%. It seems that the goal is achieved. Perform an A/B testing to check if the goal is achieved. Write precisely under which hypothesis you construct the test.
Could you help me to construct the Null and Alternative Hypotheses?

 

[Karabiner]

Due to the extremely low sample sizes, and therefore the very low statistical power, I'd guess
you should tell your manager that statistical testing does not make very much sense here.

With kind regards

Karabiner

 

[katxt]

What is A/B testing? Also, this doesn't seem like proportions because neither 67.3% of 9 nor 78.2% of 12 are whole numbers.

 

[hlsmith]

@katxt - A/B testing is a business term for an experiment. The typical example is that you randomly change the interface on Facebook''s homepage for just some users and compare an outcome between the two groups (i.e., group with normal interface vs. group with modified interface).

 

[katxt]

Cheers. Kat