To start this hypothesis test, let's define the null and alternative hypotheses based on the information given.

Step 1: State the Null and Alternative Hypotheses

We are given that the standard deviation for the machine should be at most 0.3 ounces. This suggests we are testing whether the actual standard deviation of the cereal box weights differs from this specified value.

Let:

• $\sigma =$ the actual standard deviation of the cereal box weights.

Null Hypothesis ($H_0$):

The equipment does not need recalibration, meaning the standard deviation is at most 0.3 ounces. $H_0: \sigma \leq 0.3$

Alternative Hypothesis ($H_a$):

The equipment needs recalibration, suggesting the standard deviation is greater than 0.3 ounces. $H_a: \sigma > 0.3$

This is a one-tailed test, as we are only concerned if the standard deviation exceeds 0.3 ounces.

Next Steps

1. Calculate the sample standard deviation from the provided data.
2. Use the Chi-Square test for variance with a 5% significance level to test the hypothesis.
3. Based on the Chi-Square test result, determine if we reject $H_0$ in favor of $H_a$ or fail to reject $H_0$.

Would you like me to proceed with the calculations?

Related Questions

1. How do you calculate the Chi-Square test statistic for variance?
2. What does a one-tailed test mean in hypothesis testing?
3. How is the critical value for a Chi-Square test determined?
4. What are Type I and Type II errors in hypothesis testing?
5. How does the sample size affect the reliability of the test?

Tip

When performing hypothesis tests involving variance or standard deviation, it’s essential to ensure the data is approximately normally distributed, as the Chi-Square test for variance assumes normality.