A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 446 gram setting. It is believed that the machine is underfilling the bags. A 38 bag sample had a mean of 444 grams. Assume the population variance is known to be 729 . A level of significance of 0.02 will be used. State the null and alternative hypotheses.

To test whether the bag filling machine is underfilling the bags, we can set up the null and alternative hypotheses as follows: - **Null Hypothesis (H0)**: The mean weight of the bags is equal to the target weight. In this case, we can state it as: \[ H_0: \mu = 446 \text{ grams} \] - **Alternative Hypothesis (H1)**: The mean weight of the bags is less than the target weight, indicating that the machine is underfilling the bags. This can be stated as: \[ H_1: \mu < 446 \text{ grams} \] In summary: - \( H_0: \mu = 446 \) - \( H_1: \mu < 446 \) This is a one-tailed test since we are specifically looking for evidence that the mean is less than 446 grams. The significance level for the test is set at 0.02.