Ron flips a coin n₁ times and Freda flips a coin n₂ times. We can assume all coin flips are fair: The coin has an equal chance of landing heads or tails. In each of the following cases, state whether inference for a difference in proportions is appropriate using the methods of this section. If so, give the mean and standard error for the distribution of the difference in proportions (p̂₁ − p̂₂) and state whether the normal approximation is appropriate.
(a) Let p̂₁ be the proportion of Ron’s flips that land heads and p̂₂ be the proportion of Freda’s flips that land heads; n₁ = 100 and n₂ = 50.

(b) Let p̂₁ be the proportion of Ron’s flips that land heads and p̂₂ be the proportion of Ron’s flips that land tails; n₁ = 100.

(c) Let p̂₁ be the proportion of Ron’s flips that land heads and p̂₂ be the proportion of Freda’s flips that land tails; n₁ = 200 and n₂ = 200.

(d) Let p̂₁ be the proportion of Ron’s flips that land tails and p̂₂ be the proportion of Freda’s flips that land tails; n₁ = 5 and n₂ = 10.