Answered: The amounts of nicotine in a certain…

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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$**Title: Analyzing Nicotine Levels in Cigarettes: A Statistical Approach** **Introduction:** This case study examines the nicotine content in a specific brand of cigarette. Historically, the nicotine amounts are normally distributed with a mean of 0.888 grams and a standard deviation of 0.297 grams. Recently, the company claims to have reduced the nicotine levels. A random sample of 32 cigarettes shows a mean nicotine amount of 0.804 grams. The goal is to determine the probability that this sample reflects a true reduction in nicotine levels. **Problem Statement:** Given that the historical mean and standard deviation have not changed, calculate the probability of randomly selecting 32 cigarettes with a mean nicotine content of 0.804 grams or less. \[ P(M < 0.804 \, \text{g}) = \] **Instructions:** - Enter your calculated probability as a number accurate to four decimal places. - You may use exact z-scores or z-scores rounded to three decimal places. **Conclusion:** Based on your result, decide whether the claim that the nicotine amount is lower is valid: - **Yes.** The probability of this data is unlikely to have occurred by chance alone. - **No.** The probability of obtaining this data is high enough to have been a chance occurrence. **Guidance:** For additional help or questions, please reach out to the instructor using the "Message instructor" option. **Action:** Click "Submit Question" after entering your response.$

Transcribed Image Text:**Title: Analyzing Nicotine Levels in Cigarettes: A Statistical Approach** **Introduction:** This case study examines the nicotine content in a specific brand of cigarette. Historically, the nicotine amounts are normally distributed with a mean of 0.888 grams and a standard deviation of 0.297 grams. Recently, the company claims to have reduced the nicotine levels. A random sample of 32 cigarettes shows a mean nicotine amount of 0.804 grams. The goal is to determine the probability that this sample reflects a true reduction in nicotine levels. **Problem Statement:** Given that the historical mean and standard deviation have not changed, calculate the probability of randomly selecting 32 cigarettes with a mean nicotine content of 0.804 grams or less. \[ P(M < 0.804 \, \text{g}) = \] **Instructions:** - Enter your calculated probability as a number accurate to four decimal places. - You may use exact z-scores or z-scores rounded to three decimal places. **Conclusion:** Based on your result, decide whether the claim that the nicotine amount is lower is valid: - **Yes.** The probability of this data is unlikely to have occurred by chance alone. - **No.** The probability of obtaining this data is high enough to have been a chance occurrence. **Guidance:** For additional help or questions, please reach out to the instructor using the "Message instructor" option. **Action:** Click "Submit Question" after entering your response.

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