7. Sampling Distributions & Confidence Intervals: Mean
Confidence Intervals for Population Mean
3:42 minutesProblem 7.3.3
Textbook Question
Red Blood Cell Count Here is a 95% confidence interval estimate of obtained by using the red blood cell counts of adult females listed in Data Set 1 “Body Data” in Appendix B:
[Image].
Identify the corresponding confidence interval estimate of and include the appropriate units.
Verified step by step guidance1
Step 1: Understand the problem. A confidence interval provides a range of values within which the true population parameter (in this case, the mean red blood cell count) is likely to fall. The problem asks us to identify the confidence interval and include the appropriate units.
Step 2: Identify the given confidence interval. Look at the provided data or image (if available) to determine the lower and upper bounds of the 95% confidence interval. These bounds represent the range of plausible values for the population mean.
Step 3: Verify the units of measurement. Red blood cell counts are typically measured in millions of cells per microliter (million/μL). Ensure that the units are consistent with the data provided.
Step 4: Write the confidence interval in proper notation. A confidence interval is typically expressed as (lower bound, upper bound) with the units included. For example, if the bounds are 4.2 and 5.4, the interval would be written as (4.2 million/μL, 5.4 million/μL).
Step 5: Interpret the confidence interval. Explain that we are 95% confident that the true mean red blood cell count for adult females falls within the specified range, and include the units in your interpretation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Confidence Interval
A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence, typically expressed as a percentage. For example, a 95% confidence interval suggests that if we were to take many samples and compute intervals, approximately 95% of those intervals would contain the true mean.
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Red Blood Cell Count
Red blood cell (RBC) count is a measure of the number of red blood cells in a given volume of blood, typically expressed in millions of cells per microliter (µL). This count is crucial for assessing an individual's overall health, as it can indicate conditions such as anemia or polycythemia, depending on whether the count is too low or too high.
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Units of Measurement
Units of measurement provide a standard for quantifying physical quantities. In the context of red blood cell counts, the common unit is millions of cells per microliter (µL), which allows for consistent reporting and comparison of results across different studies and populations.
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