Final answer:
The null hypothesis is that the bag filling machine fills at the mean weight of 409.0 grams (H0: μ = 409.0) and the alternative hypothesis is that the mean weight is less than 409.0 grams (Ha: μ < 409.0), tested at a significance level of 0.05.
Step-by-step explanation:
The question is regarding hypothesis testing in statistics, where the manufacturer wants to verify if the bag filling machine is accurately filling bags at the 409.0 gram setting.
The hypothesis test is to be conducted with a significance level of 0.05, assuming the variance is known to be 400.00.
The null hypothesis (H0) is that the machine fills the bags correctly, which means the mean weight is equal to 409.0 grams, stated as H0: μ = 409.0.
The alternative hypothesis (Ha) assumes the machine is underfilling, meaning the mean weight is less than 409.0 grams, stated as Ha: μ < 409.0.