[Solved] Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes is the large-sample \(z\) test appropriate? Show the calculations leading to your responses. a) \(H _ { 0 } : p = 0.72 , n = 25\) b) \(H _ { 0 } : p = 0.40 , n = 200\) Random: The lack of pattern or predictability in events, often referring to a selection method where each item has an equal chance of being chosen. Manic-Depressive Illness: Also known as bipolar disorder, a mental health condition characterized by extreme mood swings, including emotional highs (mania or hypomania) and lows (depression). Probability: The chance or likelihood that an event will happen, quantified as a number between 0 (impossible) and 1 (certain). Biased Coin: A modified or manipulated coin which does not have an equal probability of landing on heads or tails, thus influencing the outcome of a flip.