Impact Of Cooking On Air Particles — Harvard University

Impact Of Cooking On Air Particlesa Group Of Harvard University Sc

Impact of cooking on air particles. A group of Harvard University School of Public Health researchers studies the impact of cooking on the size of indoor air particles (Environmental Science and Technology, September 1, 2000). The decay rate (measured as ??? m/hour) for fine particles produced from oven cooking or toasting was recorded on six randomly selected days. These six measurements are shown in the table. a. Find and interpret a 95% confidence interval for the true average decay rate of fine particles produced from oven cooking or toasting. b. Explain what the phrase “95% confident” implies in the interpretation of part a. c. What must be true about the distribution of the population of decay rates for the inference to be valid.

Paper For Above instruction

The interaction between cooking practices and indoor air quality has become an increasingly important area of environmental health research. Specifically, understanding how cooking influences the concentration and size of airborne particles can shed light on potential health risks associated with indoor air pollution. The study conducted by Harvard University’s School of Public Health captures critical data regarding the decay rate of fine particles generated during oven cooking or toasting, providing a foundation to assess their impact and the reliability of statistical inferences drawn from sample data.

Introduction

Airborne particles, particularly fine particles (PM2.5), pose significant health risks due to their ability to penetrate deep into the respiratory system. Cooking activities, especially methods like oven cooking and toasting, contribute to indoor fine particle concentrations. This study investigates the decay rate of these particles, which reflects how quickly the particles settle or disperse, thereby influencing exposure levels. The goal is to estimate the true average decay rate and understand the reliability of this estimate through statistical inference.

Data and Methodology

The researchers measured the decay rate on six randomly selected days, with the data summarized in the table provided (hypothetically, as the actual data values are unspecified in this context). To estimate the true mean decay rate, a confidence interval can be constructed. This method involves calculating the sample mean and standard deviation, then applying the t-distribution approach because of the small sample size (n=6). The formula for the confidence interval is:

CI = x̄ ± t_{α/2, n-1} * (s / √n)

where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value from the t-distribution for the specified confidence level and degrees of freedom.

Part a: Calculating the Confidence Interval

Assuming known sample data, the typical steps include calculating the mean decay rate, the standard deviation, and then determining the appropriate t-score for 95% confidence with 5 degrees of freedom (df= n−1=5). Suppose the sample data yielded a mean of 2.5 hours^-1 and a standard deviation of 0.6 hours^-1. The t-score for 95% confidence and 5 df is approximately 2.571.

Calculating the margin of error:

ME = 2.571 (0.6 / √6) ≈ 2.571 0.245 ≈ 0.63

Constructing the confidence interval:

CI = 2.5 ± 0.63 = (1.87, 3.13)

This interval suggests that we are 95% confident the true average decay rate of fine particles produced from oven cooking or toasting lies between 1.87 and 3.13 hours^-1.

Part b: Interpretation of 95% Confidence

The phrase “95% confident” indicates that if the process of sampling and constructing confidence intervals were repeated numerous times, approximately 95% of those intervals would contain the true population mean decay rate. It does not mean there is a 95% probability that this particular interval contains the true mean, but rather that the method used provides a high level of reliability in estimating the population parameter over many repeated samples.

Part c: Assumptions for Valid Inference

For the statistical inference to be valid, certain assumptions must hold regarding the distribution of decay rates in the population. Primarily, the population of decay rates should be approximately normally distributed, especially given the small sample size of six days. When the population is normal, the t-distribution-based confidence interval is appropriate. If the population distribution is markedly skewed or contains significant outliers, the validity of the confidence interval and the inference may be compromised. In such cases, larger sample sizes or nonparametric methods may be necessary to obtain reliable estimates.

Additionally, the measurements should be independent, meaning that the decay rate recorded on one day does not influence the rates on other days. Random sampling of days ensures this independence, reinforcing the validity of the inference.

Conclusion

In conclusion, the statistical analysis provides an estimate of the average decay rate of fine particles generated during cooking, a key factor in assessing indoor air pollution. The constructed 95% confidence interval offers a range within which the true mean is likely to fall, assuming the population distribution is approximately normal and the data are independent. The interpretation of this interval relies heavily on the assumptions, and violations could lead to inaccurate conclusions about indoor air quality related to cooking habits.

References

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