Claudia Pena August 31, 2023 Bus 219 Book Exercises Chapter

Claudia Penaaugust 31 2023bus219book Exercises Chapter 1section 111

Describe the relevant population and determine whether the data points provided are associated with the population or the sample; classify variables as categorical or numerical with their specific type; and specify the measurement scale for given data collection scenarios.

Paper For Above instruction

In the realm of statistical analysis, understanding the foundational concepts of populations, samples, variables, and measurement scales is essential for interpreting data accurately. Each element offers insights into the nature of the information collected and how it can be analyzed to inform decisions or draw conclusions.

Analysis of the Apple iPhone 4 Reception Problem

The first scenario concerns the reception issues experienced by users of the Apple iPhone 4. The relevant population in this context comprises all individuals who own or have owned an iPhone 4, since the problem pertains to this specific product model’s performance. The survey data indicating that 2% of users experienced reception issues relates to a sample—presumably a subset of all iPhone 4 users surveyed at a local store or other location. Therefore, the 2% figure is associated with this sample, which serves as an estimate of the problem’s prevalence across the broader population.

Depression and Dementia Study

The second scenario involves research examining the correlation between depression and the development of dementia among elderly individuals. The relevant population consists of all elderly persons, possibly in a certain geographic area or demographic group, who could be at risk of developing dementia. The sample referenced includes 949 elderly individuals who participated in the study. Among these, 22% of those with depression developed dementia, and 17% of those without depression did so. The percentages—22% and 17%—are associated with this sample. They serve as sample estimates of the true proportions in the entire population of elderly persons, though further research would be required for definitive population parameters.

Stock Data Collection

To analyze Home Depot’s stock, one would obtain data for the last 12 months' monthly adjusted close prices from a reliable financial website. The data collected here are time series data because they consist of observations collected sequentially over time for the same metric—monthly stock prices. This type of data reflects changes over time for a single entity.

Observation of News Data

Reviewing the front page of The New York Times website provides unstructured data, as it includes a variety of news articles, images, headlines, and multimedia content without a predefined data format or organization. The information is presented in a narrative and multimedia form rather than a fixed, structured dataset with standardized variables.

Classification of Variables

Considering the specific variables provided:

  • a. Points scored in a football game: Numerical variable, specifically discrete, since points are counted in whole numbers (e.g., 0, 1, 2, 3, etc.).
  • b. Racial composition of a high school classroom: Categorical variable, as it categorizes students by race. It is nominal since the categories are labels with no inherent order.
  • c. Heights of 15-year-olds: Numerical variable, continuous, because height can be measured at any level within a range (e.g., 150.5 cm, 152.3 cm).

Measurement Scales Analysis

For the scenarios involving measurement scales:

  1. a. Weekly gold closing prices: Ratio scale, as gold prices are numerical with a meaningful zero point and ratios can be computed (e.g., $1,200 is twice $600).
  2. b. Bond credit ratings (AAA, AA, BBB, BB, CC, D): Ordinal scale, since these categories have a clear order of increasing risk but no fixed numerical difference between them.
  3. c. Student major categories: Nominal scale, as categories such as accounting or finance are labels without inherent order or ranking.

Conclusion

Understanding whether data describes populations or samples, identifying variable types, and recognizing measurement scales are fundamental skills in statistics that enable accurate data analysis and interpretation. Whether assessing consumer product performance, medical research outcomes, stock market trends, or survey data, these concepts guide the correct application of statistical techniques and ensure valid conclusions.

References

  • Frankfort-Nachmias, C., & Nachmias, D. (2008). Research Methods in the Social Sciences. Worth Publishers.
  • Levin, R. I., & Rubins, D. (2002). Statistics for Management. Pearson.
  • Trochim, W. M. K. (2006). Research Methods Knowledge Base. Atomic Dog Publishing.
  • Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
  • Ross, S. M. (2014). Introduction to Probability and Statistics. Academic Press.
  • Devore, J. L. (2011). Probability and Statistics for Engineering and the Sciences. Brooks Cole.
  • Bickel, P., & Doksum, K. (2015). Mathematical Statistics: Basic Ideas and Selected Topics. CRC Press.
  • Hogget, R. (2013). Data Analysis for Business Decisions. Wiley.
  • Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2016). Statistics for Business and Economics. Cengage Learning.
  • Mendenhall, W., Ott, L., & Sincich, T. (2012). A First Course in Statistics. Pearson.

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