3. We have the formula for a linear combination of random variables that ? 2 aX+bY = a 2? 2 X + b 2? 2 Y which we have used several times (the more familiar standard deviation is simply the square root). In doing inference for p1 ? p2, (i.e. comparing the proportions for two different populations), there are two formulas that might be used (derived from the above 1 formula). They are: ? 2 p?1?p?2 = p?1(1 ? p?1) n1 + p?2(1 ? p?2) n2 and ? 2 p?1?p?2 = ?p ? (1 ? p? ? )( 1 n1 + 1 n2 ) where ?p ? = x1+x2 n1+n2 = n1p?1+n2p?2 n1+n2 .

a. Give an example of a study/experiment where this (p1 ? p2) would be your parameter of interest.

b. One of these formulas is appropriate for confidence intervals and the other is appropriate for hypotheses testing. Which is which? Your answer should make a connection between the definition of ?p ? and the definition of the p-value, (what must be assumed so that ?p ? is a reasonable quantity to compute and when do we assume that?).

3. We have the formula for a linear combination of random variables that "axtby = alok + bro? which we have used several times (the more familiar standard deviation is simply the square root). In doing inference for p1 - p2, (i.e. comparing the proportions for two different populations), there are two formulas that might be used (derived from the above formula). They are: pi(1 - p1) p2(1 - p2) n1 n2 and Up1 -pa = P* (1 - p* ) (-+ n1 n2 where p* = Ditzy _ nipitnap2 n1+712 n1+72 a. Give an example of a study/experiment where this (p1 - p2) would be your parameter of interest. b. One of these formulas is appropriate for confidence intervals and the other is appropriate for hypotheses testing. Which is which? Your answer should make a connection between the definition of p* and the definition of the p-value, (what must be assumed so that p* is a reasonable quantity to compute and when do we assume that?)