Math Problem Statement

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 overfilled? Based on a 33 bag sample, the manufacturer decides to reject the null hypothesis.

What is the conclusion?

Solution

Given the information provided, here’s how we interpret the situation:

  1. Null Hypothesis H0H_0: The filling machine fills the bags correctly, meaning the mean weight of the bags is 426 grams.

  2. Alternative Hypothesis H1H_1: The filling machine overfills the bags, meaning the mean weight of the bags is greater than 426 grams.

  3. Significance Level: The test is conducted at a 0.02 significance level.

Since the manufacturer decided to reject the null hypothesis, it means that the test provided sufficient evidence to conclude that the bags are indeed overfilled, based on the data from the 33-bag sample.

Conclusion

At the 0.02 significance level, there is sufficient evidence to conclude that the bags are overfilled, as the sample data led to the rejection of the null hypothesis.

Would you like a deeper explanation or have any further questions?

Here are some related questions to consider:

  1. What type of statistical test could be used to test for overfilling?
  2. What assumptions are necessary to conduct this test?
  3. How would changing the significance level to 0.05 affect the test results?
  4. How would the conclusion change if the test failed to reject the null hypothesis?
  5. What sample size might be required for higher confidence?

Tip: When interpreting hypothesis test results, always check the significance level and ensure it aligns with the strength of evidence you need.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Statistical Significance
One-Sided Test

Formulas

Z-test formula for sample mean: Z = (X̄ - μ) / (σ / √n)

Theorems

Central Limit Theorem

Suitable Grade Level

College-level Statistics