1. The problem asks to state the null hypothesis for testing the claim that a population mean equals 40. 2. The null hypothesis, denoted as $H_0$, is a statement of no effect or no difference. It is the claim we test against. 3. For testing a population mean, the null hypothesis is usually that the population mean equals the claimed value. 4. Therefore, the null hypothesis is: $$H_0: \mu = 40$$ 5. This means we assume the population mean $\mu$ is 40 unless evidence suggests otherwise. 6. The alternative hypothesis $H_a$ would be that $\mu \neq 40$, $\mu > 40$, or $\mu < 40$ depending on the test type, but the question only asks for the null hypothesis. Final answer: $$H_0: \mu = 40$$