**Case Study: Testing the Mean Amount of Paint in 1-Gallon Cans**A paint supply store manager wishes to verify if the mean volume of paint per 1-gallon can meets the manufacturer’s specification. The goal is to determine if the actual mean volume matches the advertised figure of 1.0 gallon.### Testing Process:1. **Sample Data:** - A sample of 55 cans is selected. - The mean amount of paint in the sample is 0.995 gallon. - Standard deviation given by the manufacturer is 0.009 gallon.2. **Confidence Interval Calculation:** - The 99.19% confidence interval is calculated to be: 0.9919 ≤ μ ≤ 0.9981 (rounded to four decimal places).3. **Hypothesis Testing:** - Null Hypothesis (H₀): The mean volume is 1.0 gallon. - Conclusion Methods: - **A:** Reject H₀: Value 1.0 is within the confidence interval. - **B:** Fail to reject H₀: Value 1.0 is outside the confidence interval. - **C:** Fail to reject H₀: Value 1.0 is within the confidence interval. - **D:** Reject H₀: Value 1.0 is outside the confidence interval. - **Correct Conclusion: D.** Reject H₀, as 1.0 gallon is outside the confidence interval.4. **Comparison of Results:** - Comparing results from parts (a) and (c), we find: - **No,** the results are not the same.5. **Effect of Different Standard Deviation:** - With a standard deviation of 0.030: - Zₛₜₐₜ = -1.24, p-value = 0.216 - 99% confidence interval is 0.9846 ≤ μ ≤ 1.0054. - Using a critical value approach: Compare if Zₛₜₐₜ has increased or decreased in absolute value compared to part (a).This study aids in understanding the methodology behind testing sample means against known specifications, using confidence intervals and hypothesis testing.

We have given that e) standard deviation sigma =0.030 , ZSTAT= -1.24 and p-value =0.216 99%…

Answered: e. Compare the results of parts (a)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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