A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 426
 gram setting.  Is there sufficient evidence at the 0.02
 level that the bags are underfilled?  Assume the population is normally distributed.

State the null and alternative hypotheses for the above scenario.

To determine if there is sufficient evidence that the bags are underfilled, we can set up the null and alternative hypotheses as follows:

1. **Null Hypothesis (H₀):** The machine is filling the bags correctly at the 426-gram setting.
   \[
   H_0: \mu = 426
   \]
   where \(\mu\) is the true mean weight of the bags filled by the machine.

2. **Alternative Hypothesis (H₁):** The machine is underfilling the bags.
   \[
   H_1: \mu < 426
   \]

In this case, since we are testing if the bags are underfilled (specifically less than 426 grams), we use a one-tailed test with the alternative hypothesis \(H_1: \mu < 426\). The significance level (\(\alpha\)) is 0.02.

Would you like to proceed with the steps for testing this hypothesis or need further assistance on this? 

Here are some related questions you might find helpful:

1. How do we determine if the machine’s output is normally distributed?
2. What is the critical value for a one-tailed test at the 0.02 significance level?
3. How is the sample mean used in hypothesis testing in this context?
4. What role does the standard deviation play in testing the mean?
5. What type of error could occur if we incorrectly reject the null hypothesis?

**Tip:** In hypothesis testing, remember that the null hypothesis is typically a statement of no effect or no difference, which we test against an alternative hypothesis.

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 426-gram setting. Is there sufficient evidence at the 0.02 level that the bags are underfilled? Assume the population is normally distributed.

Determine if there is enough evidence at the 0.02 significance level to conclude that a banana chip bag filling machine underfills at the 426-gram setting. This problem explores hypothesis testing with a one-tailed test, using normal distribution principles, and is suitable for introductory statistics students.

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