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(a) Define a relevant parameter of interest, using correct notation. (b) Use the bootstrap distribution to estimate the sample statistic, including correct notation. (c) Use the bootstrap distribution to estimate a 99% confidence interval. (d) Interpret this interval in context. (e) Does this interval provide evidence that con- centrations of the pesticide 3-PBA are lower while eating organic? Why or why not? (f) Can we conclude that eating organic causes lower concentrations of 3-PBA? Why or why not? 15 MINI 20 25 24.518 30 35 Figure 3.34 Bootstrap distribution based on 1000 simulations for Exercise 3.130 ..

(a) Define a relevant parameter of interest, using correct notation. (b) Use the bootstrap distribution to estimate the sample statistic, including correct notation. (c) Use the bootstrap distribution to estimate a 99% confidence interval. (d) Interpret this interval in context. (e) Does this interval provide evidence that con- centrations of the pesticide 3-PBA are lower while eating organic? Why or why not? (f) Can we conclude that eating organic causes lower concentrations of 3-PBA? Why or why not? 15 MINI 20 25 24.518 30 35 Figure 3.34 Bootstrap distribution based on 1000 simulations for Exercise 3.130 ..

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Can you explain 3.130 part a and b? Thank you
**Title: Using Bootstrap Distributions to Estimate and Interpret Data** **Section: Exercise on Confidence Intervals and Bootstrap Distribution** **Page 273** 1. **Define a Relevant Parameter:** - Identify a parameter of interest and express it using correct statistical notation. 2. **Estimate the Sample Statistic Using Bootstrap:** - Utilize the bootstrap distribution to approximate the sample statistic. Ensure that correct statistical notation is used. 3. **Estimate a 99% Confidence Interval:** - Apply the bootstrap distribution to calculate a 99% confidence interval for the parameter. 4. **Interpret the Confidence Interval:** - Contextualize and explain the meaning of the confidence interval within the given scenario. 5. **Evaluate Evidence from the Interval:** - Determine whether the interval shows that concentrations of the pesticide 3-PBA are lower when eating organic. Provide a rationale for your answer. 6. **Draw Conclusions on Organic Eating and Pesticide Concentration:** - Assess whether it can be concluded that consuming organic foods results in lower 3-PBA concentrations. Explain your reasoning. **Figure 3.34: Bootstrap Distribution** - **Description:** - The figure displays a bootstrap distribution of a dataset based on 1000 simulations. This histogram represents the variability of the sample statistic for Exercise 3.130. - The distribution appears slightly right-skewed, with the peak around 24.518 and values ranging from approximately 10 to 40. **Note:** This exercise helps in understanding how bootstrap methods can be employed in statistics to estimate parameters and draw inferences about data confidently.
Transcribed Image Text:**Title: Using Bootstrap Distributions to Estimate and Interpret Data** **Section: Exercise on Confidence Intervals and Bootstrap Distribution** **Page 273** 1. **Define a Relevant Parameter:** - Identify a parameter of interest and express it using correct statistical notation. 2. **Estimate the Sample Statistic Using Bootstrap:** - Utilize the bootstrap distribution to approximate the sample statistic. Ensure that correct statistical notation is used. 3. **Estimate a 99% Confidence Interval:** - Apply the bootstrap distribution to calculate a 99% confidence interval for the parameter. 4. **Interpret the Confidence Interval:** - Contextualize and explain the meaning of the confidence interval within the given scenario. 5. **Evaluate Evidence from the Interval:** - Determine whether the interval shows that concentrations of the pesticide 3-PBA are lower when eating organic. Provide a rationale for your answer. 6. **Draw Conclusions on Organic Eating and Pesticide Concentration:** - Assess whether it can be concluded that consuming organic foods results in lower 3-PBA concentrations. Explain your reasoning. **Figure 3.34: Bootstrap Distribution** - **Description:** - The figure displays a bootstrap distribution of a dataset based on 1000 simulations. This histogram represents the variability of the sample statistic for Exercise 3.130. - The distribution appears slightly right-skewed, with the peak around 24.518 and values ranging from approximately 10 to 40. **Note:** This exercise helps in understanding how bootstrap methods can be employed in statistics to estimate parameters and draw inferences about data confidently.
**Eating Organic and 3-PBA Levels** We first study 3-PBA, a commonly used insecticide found in grains, fruits, and vegetables. How much higher are 3-PBA concentrations while not eating organic versus eating organic? A bootstrap distribution based on 1000 samples of the mean concentration before the switch minus the mean concentration after switching to organic is shown in Figure 3.34. **References:** - Mata, J., Frank, R., and Gigerenza, G., “Symptom Recognition of Heart Attack and Stroke in Nine European Countries: A Representative Survey”, *Health Expectations*, 2012; doi: 10.1111/j.1369-7625.2011.00764.x. - Magner, J., Wallberg, P., Sandberg, J., and Cousins, A.P. (2015). “Human exposure to pesticides from food: A pilot study,” *IVL Swedish Environmental Research Institute*. https://www.coop.se/PageFiles/429812/Coop%20Ekoeffekten_Report%20ENG.pdf, January 2015. - For illustrative purposes we will assume the measurements were far enough apart to be unrelated. - [YouTube Link](https://www.youtube.com/watch?v=oB6fQuymyKC8).
Transcribed Image Text:**Eating Organic and 3-PBA Levels** We first study 3-PBA, a commonly used insecticide found in grains, fruits, and vegetables. How much higher are 3-PBA concentrations while not eating organic versus eating organic? A bootstrap distribution based on 1000 samples of the mean concentration before the switch minus the mean concentration after switching to organic is shown in Figure 3.34. **References:** - Mata, J., Frank, R., and Gigerenza, G., “Symptom Recognition of Heart Attack and Stroke in Nine European Countries: A Representative Survey”, *Health Expectations*, 2012; doi: 10.1111/j.1369-7625.2011.00764.x. - Magner, J., Wallberg, P., Sandberg, J., and Cousins, A.P. (2015). “Human exposure to pesticides from food: A pilot study,” *IVL Swedish Environmental Research Institute*. https://www.coop.se/PageFiles/429812/Coop%20Ekoeffekten_Report%20ENG.pdf, January 2015. - For illustrative purposes we will assume the measurements were far enough apart to be unrelated. - [YouTube Link](https://www.youtube.com/watch?v=oB6fQuymyKC8).
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