How to formulate a null hypothesis?

[TytoAlba95]

Summary:: The correct answer to Q67 is (a).

How to formulate a null hypothesis when we have some data and we want to check if it obeys Recessive epistasis ratio, 9:7.
Doesn't null hypothesis, always assumes that there's no difference between the Obs and Exp values, all differences are due to chance or error? Isn't the alternative hypothesis which assumes the desired ratio?
# Though my question is inspired by this MCQ, but it is not the MCQ itself. So instead of homework I have posted this thread here.

 

[FactChecker]

Summary:: The correct answer to Q67 is (a).

How to formulate a null hypothesis when we have some data and we want to check if it obeys Recessive epistasis ratio, 9:7.
Doesn't null hypothesis, always assumes that there's no difference between the Obs and Exp values, all differences are due to chance or error?

Yes.

Isn't the alternative hypothesis which assumes the desired ratio?

I don't think so. The alternative hypothesis is just that the null hypothesis is not true. If the null hypothesis were true, the observed results would be very strange luck. I don't understand the problem well enough to say what that means in terms of a ratio of 9:7. My guess is that the 9:7 ratio would be used to determine the expected values. So the null hypothesis would be that the observed values are close enough to the expected values to believe that the theoretical ratio of 9:7 may hold.

 

[Stephen Tashi]

Doesn't null hypothesis, always assumes that there's no difference between the Obs and Exp values, all differences are due to chance or error?

The only requirement for a null hypothesis is that it must allow us to calculate the probability of the observed data.

It is correct that a null hypothesis often assumes the data is generated by some probability model that assumes two or more aspects of the data do not affect the outcomes. However, there can be cases where different aspects are expected to affect probabilities differently in some definite way.

For example, the usual null hypothesis in a coin-tossing experiment would be that the coin is "fair" so the two aspects "Heads" and "Tails" do no change the probability of how the coin lands - both having probability 1/2. This hypothesis is sufficient to compute probabilities for the outcomes of a statistical test such as "The probability that in 10 tosses, we get 8 or more Heads, or 2 or less Heads".

A hypothesis such as "The coin is not fair" is not specific enough to allow us to compute the probabilities for the outcomes of a statistical test.

However, suppose we run an "unfair" coin manufacturing factory and our goal is to manufacture coins that have a probability of 2/3 of landing Heads. To test if a coin achieves this goal, we could use the null hypothesis "The probability that the coin lands heads is 2/3". In such a situation we want to reject coins that are fair, but we also want to reject coins where the probability of landing heads is 1/8 or 9/10 etc.