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Determining the null hypothesis and its effect.

Determining the null hypothesis and its effect.

Super Learner
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Hi,
I still don’t understand the concept of determining the null hypothesis and its effect on the calculation. In the video I linked below there is the following exercise: “Ajax releases a new dish detergent, called Extreme Ajax+, which they advertise to be able to clean many more dishes with a single bottle.” Then you say that H0: μExtremeAjax+ – μAjax ≤ 0. What if Ajax claimed that Ajax+ did not work? In this case the data set would be the same but we have a different conlusion? It does not make sense to me. Then H0 would be: μExtremeAjax+ – μAjax > 0? No matter what the null hypothesis is I got a P value of 0.00964. The problem is that in the first case we reject the null hypothesis and say that Ajax+ is better, and in the second case we also reject the null hypothesis, but in this case it means that Ajax+ is not working, in spite of the fact that the data set is exactly the same so we got a paradox. 
So my question is the following: If the H0 is the opposite (because Ajax says an opposite claim), do we get a different P-value? Does the null hypothesis have any effect on our calculation, and if yes, how because I got the same P-value? 
Thanks in advance :).
GB

1 Answer

Super Learner
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Please guys, answer this question, because I cannot proceed. How does the P-value change if the null hypothesis is the exact opposite? Because, whenever I calculate it, I get the same P-value for the exact opposite null hypothesis, and that is a paradox.
Thanks.