Nicotine in Cigarettes Some of the nonparametric methods in this chapter use ranks of data. Find the ranks corresponding to the following amounts (milligrams) of nicotine in king-sized cigarettes (from Data Set 16 “Cigarette Contents” in Appendix B).

1.1 1.7 1.7 1.1 1.4 1.0 1.2 1.8 1.6 1.1

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Step 1: Understand the concept of ranking data. Ranking involves ordering the data values from smallest to largest and assigning ranks accordingly. If there are ties (identical values), assign the average of the ranks that would have been assigned to those values.

Step 2: Arrange the given nicotine amounts in ascending order: 1.0, 1.1, 1.1, 1.1, 1.2, 1.4, 1.6, 1.7, 1.7, 1.8.

Step 3: Assign ranks to the values. Start with rank 1 for the smallest value and increase the rank for each subsequent value. For tied values, calculate the average rank for the tied positions. For example, if three values are tied and would occupy ranks 2, 3, and 4, assign each of them the average rank (2+3+4)/3 = 3.

Step 4: Replace each original nicotine amount with its corresponding rank. Ensure that tied values are assigned the same rank (average rank for tied positions).

Step 5: Verify the ranks to ensure they are correctly assigned and correspond to the original data values. Double-check for accuracy in handling ties and ordering.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ranking Data

Ranking data involves ordering values from smallest to largest and assigning a rank to each value based on its position in this order. In cases of ties, where multiple values are the same, each tied value receives the average of the ranks they would occupy. This method is essential in nonparametric statistics, as it allows for analysis without assuming a specific distribution of the data.

Nonparametric Methods

Nonparametric methods are statistical techniques that do not assume a specific distribution for the data, making them useful for analyzing ordinal data or data that do not meet the assumptions of parametric tests. These methods often rely on ranks rather than raw data values, allowing for robust analysis in situations where traditional methods may fail due to violations of assumptions.

Data Set and Context

Understanding the context of a data set is crucial for proper analysis. In this case, the data set refers to nicotine content in cigarettes, which provides a specific context for the ranks being calculated. Recognizing the source and nature of the data helps in interpreting the results and understanding their implications in real-world scenarios, such as public health and smoking regulations.

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