1. The problem asks us to state the null hypothesis for testing the claim that 9 out of 10 doctors recommend aspirin, i.e., the population proportion $p=0.9$. 2. The null hypothesis ($H_0$) is a statement of no effect or no difference, usually an equality. It represents the claim we want to test. 3. The alternative hypothesis ($H_a$) represents what we want to provide evidence for, and it can be one-sided or two-sided. 4. Since the claim is that the proportion is 0.9, the null hypothesis is: $$H_0: p = 0.9$$ 5. The alternative hypothesis could be: - $H_a: p \neq 0.9$ (two-sided) - $H_a: p > 0.9$ (greater than) - $H_a: p < 0.9$ (less than) 6. The question asks specifically for the null hypothesis, so the correct answer is: **The proportion of doctors recommending aspirin is equal to 0.9.**