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(c) Interpret this interval in context. 0.25 0.40 0.45 Figure 3.35 Bootstrap distribution for the difference in proportions 0.30 0.35

(c) Interpret this interval in context. 0.25 0.40 0.45 Figure 3.35 Bootstrap distribution for the difference in proportions 0.30 0.35

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
Problem 1P
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Can you explain 3.133 part c?
**Sample Difference in Proportions** Calculate the sample difference in proportions: proportion of measurements resulting in pesticide detection while eating non-organic minus proportion of measurements resulting in pesticide detection while eating organic. **Bootstrap Distribution** Figure 3.35 provides a bootstrap distribution for the difference in proportions, based on 1000 simulated bootstrap samples. Approximate a 98% confidence interval. **Interpretation** Interpret this interval in context. **Figure 3.35 Explanation** The figure shows a histogram representing the bootstrap distribution for the difference in proportions of pesticide detection between non-organic and organic consumption. The distribution is approximately normal, with most of the values centered around 0.35. The x-axis ranges from 0.25 to 0.45, indicating the range of observed differences. This visualization helps in understanding the variability and confidence interval for the observed difference in proportions.
Transcribed Image Text:**Sample Difference in Proportions** Calculate the sample difference in proportions: proportion of measurements resulting in pesticide detection while eating non-organic minus proportion of measurements resulting in pesticide detection while eating organic. **Bootstrap Distribution** Figure 3.35 provides a bootstrap distribution for the difference in proportions, based on 1000 simulated bootstrap samples. Approximate a 98% confidence interval. **Interpretation** Interpret this interval in context. **Figure 3.35 Explanation** The figure shows a histogram representing the bootstrap distribution for the difference in proportions of pesticide detection between non-organic and organic consumption. The distribution is approximately normal, with most of the values centered around 0.35. The x-axis ranges from 0.25 to 0.45, indicating the range of observed differences. This visualization helps in understanding the variability and confidence interval for the observed difference in proportions.
**3.133 What Proportion Have Pesticides Detected?** In addition to the quantitative variable pesticide concentration, the researchers also report whether or not the pesticide was detected in the urine (at standard detection levels). Before the participants started eating organic, 111 of the 240 measurements (combining all pesticides and people) yielded a positive pesticide detection. While eating organic, only 24 of the 240 measurements resulted in a positive pesticide detection. --- **(a)** Calculate the sample difference in proportions: the proportion of measurements resulting in pesticide detection while eating non-organic minus the proportion of measurements resulting in pesticide detection while eating organic. **(b)** Figure 3.35 gives a bootstrap distribution for the difference in proportions, based on 1000 simulated bootstrap samples. Approximate a 98% confidence interval. **(c)** Interpret this interval in context. --- ### Explanation of Figure 3.35 The figure below (not fully visible in the image) is described as a bootstrap distribution for the difference in proportions. Bootstrapping is a method for estimating the sampling distribution of a statistic by resampling with replacement from the data. This distribution helps to approximate a confidence interval, which in this case is for the difference in the detection of pesticides between non-organic and organic diets based on the observed sample data.
Transcribed Image Text:**3.133 What Proportion Have Pesticides Detected?** In addition to the quantitative variable pesticide concentration, the researchers also report whether or not the pesticide was detected in the urine (at standard detection levels). Before the participants started eating organic, 111 of the 240 measurements (combining all pesticides and people) yielded a positive pesticide detection. While eating organic, only 24 of the 240 measurements resulted in a positive pesticide detection. --- **(a)** Calculate the sample difference in proportions: the proportion of measurements resulting in pesticide detection while eating non-organic minus the proportion of measurements resulting in pesticide detection while eating organic. **(b)** Figure 3.35 gives a bootstrap distribution for the difference in proportions, based on 1000 simulated bootstrap samples. Approximate a 98% confidence interval. **(c)** Interpret this interval in context. --- ### Explanation of Figure 3.35 The figure below (not fully visible in the image) is described as a bootstrap distribution for the difference in proportions. Bootstrapping is a method for estimating the sampling distribution of a statistic by resampling with replacement from the data. This distribution helps to approximate a confidence interval, which in this case is for the difference in the detection of pesticides between non-organic and organic diets based on the observed sample data.
Expert Solution
Step 1

The bootstrapping procedure essentially considers multiple resamples (with replacement) for a considered set of observations. The distribution of the simulated samples can be interpreted to derive the true value of the parameter (i.e., the population parameter) with a certain degree of precision. 

In this case, the parameter of interest is the "proportion difference between the detected pesticide in urine before and after eating organic". The desired level of surety (or preciseness) is 98%. 

 

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