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Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 Whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 Whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 Whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 Whites. Find the probability that the person was Latino.

Step by step solution

01

Total Smokers

First, calculate the total number of smokers. Add all the smokers from each ethnic group and each smoking level together.For all levels and ethnicities:\[\text{Total Smoker Count} = 9886 + 2745 + 12831 + 8378 + 7650 + 6514 + 3062 + 4932 + 10680 + 9877 + 1671 + 1419 + 1406 + 4715 + 6062 + 759 + 788 + 800 + 2305 + 3970 \]This equals 132,015.

02

Total Latino Smokers

Calculate the total number of Latino smokers across all smoking levels.\[\text{Total Latino Count} = 12831 + 4932 + 1406 + 800 = 19,969\]

03

Finding the Probability

The probability of a randomly selected smoker being Latino is the total number of Latino smokers divided by the total number of smokers calculated in Step 1.\[P(\text{Latino}) = \frac{19969}{132015}\]Simplifying the fraction gives approximately 0.1512 or 15.12%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ethnicity in Statistics

In statistics, ethnicity refers to the classification of people based on common cultural, national, tribal, religious, or linguistic traits. It's crucial for comprehending diverse socio-economic and health trends. For example, understanding ethnic variations helps researchers identify health disparities among different groups, which can be important in public health studies.
In research, ethnicity is often self-reported and incorporated into data sets as an important demographic variable. By analyzing ethnic data, statisticians can detect patterns and develop models to predict outcomes or identify risk factors prevalent in different ethnic groups. This becomes essential in tailoring public health policies.
In our exercise about smoking habits, ethnicity helps us see how different groups have varying smoking levels. This information can guide public health interventions by targeting ethnic groups with higher smoking rates to reduce smoking-related diseases.

Smoking Levels Statistics

Smoking levels refer to the classification of smokers based on the number of cigarettes they consume daily. Typically categorized as light, moderate, or heavy smokers, understanding these statistics is crucial in health-related studies.
Smoking levels statistics can identify trends, such as changes in smoking behavior over time or differences in consumption among various demographic groups. In our scenario, distinguishing smokers by levels—such as those smoking 10, 20, or even more cigarettes daily—provides insight into smoking habits. It can show where interventions might be most needed.

• Light smokers: 1-10 cigarettes daily.
• Moderate smokers: 11-20 cigarettes daily.
• Heavy smokers: 21+ cigarettes daily.

With detailed statistics on smoking levels, researchers can identify risk patterns and potential health outcomes related to different levels of tobacco exposure.

Data Analysis in Research

Data analysis is the process of examining, cleaning, transforming, and modeling data to discover useful information, inform conclusions, and support decision-making. In research, it helps to make sense of extensive data sets.
Using data analysis, statisticians can calculate probabilities, detect trends, and establish correlations between variables. For instance, in our given data, we used data analysis to determine the probability of a smoker being Latino by dividing the number of Latino smokers by the total number of smokers. This type of analysis is crucial for making informed decisions and deriving insights from complex datasets.

• Steps: Define the problem, gather data, apply statistical methods, interpret the results, and report findings.
• Tools: Software like R, Python, or SPSS is often used for complex calculations and visualizations.

Effective data analysis transforms raw data into meaningful information, driving research conclusions and influencing policy-making.