Estimate The Mean: Data From 28 Heart Patients

Estimate the mean, you collect data from 28 heart patients. Justify for full credit

The assignment asks to determine which of the listed options correctly defines the sample and variable in a study involving cholesterol levels of 28 heart patients. The core approach involves understanding the distinction between a sample (a subset of a population) and a variable (a characteristic measured). The correct identification is based on statistical definitions: a sample is a subset of individuals from a larger population, and a variable is a measurable characteristic that can vary across individuals.

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In the context of statistical analysis, understanding the fundamental concepts of sample and variable is crucial when designing studies and analyzing data. For the scenario where data is collected from 28 heart patients regarding their cholesterol levels, it is important to accurately categorize the sample and variable to ensure correct data analysis and interpretation.

Part (a) of the question asks to identify which option correctly describes the sample. The options provided are as follows:

  • (i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two days ago
  • (ii) Cholesterol level of the person recovering from a heart attack suffered two days ago
  • (iii) Set of all patients recovering from a heart attack suffered two days ago
  • (iv) Set of 28 patients recovering from a heart attack suffered two days ago

The most appropriate choice is option (iv): "Set of 28 patients recovering from a heart attack suffered two days ago." This option correctly identifies the sample as the specific, finite group of 28 patients from whom data was collected. It represents a subset of the population (all heart patients recovering from a heart attack), that is, the actual group studied.

Option (i) refers to the mean cholesterol levels, which is a calculated summary statistic rather than a description of the sample itself. Option (ii) refers to a single individual, which is irrelevant for the sample definition. Option (iii) refers to the entire population of such patients, not the specific sample studied.

Part (b) asks to identify the variable among the options listed. The options are:

  • (i) Mean cholesterol levels of 28 patients recovering from a heart attack suffered two days ago
  • (ii) Cholesterol level of the person recovering from a heart attack suffered two days ago
  • (iii) Set of all patients recovering from a heart attack suffered two days ago
  • (iv) Set of 28 patients recovering from a heart attack suffered two days ago

The most relevant answer is (ii): "Cholesterol level of the person recovering from a heart attack suffered two days ago." A variable is a characteristic that can differ between individuals, and in this context, the cholesterol level is a measurable characteristic that varies among patients.

Options (i), (iii), and (iv) describe the statistic or the group of individuals, not the characteristic being measured. Therefore, the variable here is the cholesterol level of a patient, which can take different values among patients.

In conclusion, selecting the correct options is based on the foundational definitions in statistics: the sample is the specific group studied, and the variable is the characteristic measured from that group.

References

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  • Bickel, P. J., & Doksum, K. A. (2015). Mathematical Statistics: Basic Ideas and Selected Topics. CRC Press.

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