A can of soda is labeled as containing 16 fluid ounces. The quality control manager wants to verify that the filling machine is neither over-fillind Next question cans. Complete parts (a) through (d) below. (a) Determine the null and alternative hypotheses that would be used to determine if the filling machine is calibrated correctly. Họ: H,: (Type integers or decimals. Do not round.) (b) The quality control manager obtains a sample of 80 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test. There V sufficient evidence to conclude that the machine is out of calibration. (c) Suppose, in fact, the machine is not out of calibration. Has a Type I or Type Il error been made? V has been made since the sample evidence led the quality-control manager to V the null hypothesis, when the is true. (d) Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of significance would you recommend quality control manager to use? Explain. The level of significance should be V because this makes the probability of Type I error

MATLAB: An Introduction with Applications
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**Title: Quality Control for Soda Filling Machine: Hypothesis Testing**

A can of soda is labeled as containing 16 fluid ounces. The quality control manager wants to verify that the filling machine is neither over-filling nor under-filling the cans. Complete parts (a) through (d) below.

---

**(a) Determine the null and alternative hypotheses for testing if the filling machine is calibrated correctly.**

- **H₀ (Null Hypothesis):** μ = [ ]
- **H₁ (Alternative Hypothesis):** μ ≠ [ ]

*(Type integers or decimals. Do not round.)*

---

**(b) Sample Evidence and Conclusion**

The quality control manager obtains a sample of 80 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test.

There [ ] sufficient evidence to conclude that the machine is out of calibration.

---

**(c) Error Analysis**

Suppose, in fact, the machine is not out of calibration. Has a Type I or Type II error been made?

A [ ] error has been made since the sample evidence led the quality-control manager to [ ] the null hypothesis, when the [ ] is true.

---

**(d) Recommendation for Level of Significance**

Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of significance would you recommend the quality control manager to use? Explain.

The level of significance should be [ ] because this makes the probability of Type I error [ ].

---

**Explanation of Missing Parts:**

- **Null and Alternative Hypotheses (a):** Typically, μ = 16 is used for the null hypothesis, indicating the machine is correctly calibrated. The alternative hypothesis, μ ≠ 16, indicates the machine is not correctly calibrated.
- **Type of Error (c):** A Type I error occurs when the null hypothesis is rejected when it is true, and a Type II error occurs when the null hypothesis is not rejected when it is false.
- **Level of Significance (d):** A smaller level of significance (e.g., 0.01) reduces the probability of a Type I error, as management prefers a higher confidence to act upon out-of-calibration evidence.

This example involves statistical decision-making and trade-offs in hypothesis testing, commonly used in quality control to maintain product standards.
Transcribed Image Text:**Title: Quality Control for Soda Filling Machine: Hypothesis Testing** A can of soda is labeled as containing 16 fluid ounces. The quality control manager wants to verify that the filling machine is neither over-filling nor under-filling the cans. Complete parts (a) through (d) below. --- **(a) Determine the null and alternative hypotheses for testing if the filling machine is calibrated correctly.** - **H₀ (Null Hypothesis):** μ = [ ] - **H₁ (Alternative Hypothesis):** μ ≠ [ ] *(Type integers or decimals. Do not round.)* --- **(b) Sample Evidence and Conclusion** The quality control manager obtains a sample of 80 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test. There [ ] sufficient evidence to conclude that the machine is out of calibration. --- **(c) Error Analysis** Suppose, in fact, the machine is not out of calibration. Has a Type I or Type II error been made? A [ ] error has been made since the sample evidence led the quality-control manager to [ ] the null hypothesis, when the [ ] is true. --- **(d) Recommendation for Level of Significance** Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of significance would you recommend the quality control manager to use? Explain. The level of significance should be [ ] because this makes the probability of Type I error [ ]. --- **Explanation of Missing Parts:** - **Null and Alternative Hypotheses (a):** Typically, μ = 16 is used for the null hypothesis, indicating the machine is correctly calibrated. The alternative hypothesis, μ ≠ 16, indicates the machine is not correctly calibrated. - **Type of Error (c):** A Type I error occurs when the null hypothesis is rejected when it is true, and a Type II error occurs when the null hypothesis is not rejected when it is false. - **Level of Significance (d):** A smaller level of significance (e.g., 0.01) reduces the probability of a Type I error, as management prefers a higher confidence to act upon out-of-calibration evidence. This example involves statistical decision-making and trade-offs in hypothesis testing, commonly used in quality control to maintain product standards.
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