What was the source formula for deriving sample size? How did we find it?

And why do we need coefficient k?

Hi @emissaryprog!

The formula for sample size is derived from the restriction on beta.

The idea behind the derivation is that for a given alpha, you can define the test based on critial values. The decision will depend on the number of samples n (because the test statistic depends on it).

Once you have that decision rule based on the critical value, you can find the type II error for any particular value of the parameter within the alternative hypothesis. If you fix the probability of error for that value of theta (beta) then you can find the number of samples needed to satify that restriction (in addition to the significance level you used to find the critical value). It is a bit tedious, but if you follow all the math, you get to the expression showed in the assignment.

Regarding the value k, it is a smart way to link the two sample sizes (n1 and n2) so that you can write n2 as a function of n1, which simplifies derivations.

Hope this helps clarify your concerns.

Cheers!

Magui