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Ch. 7 - Estimating Parameters and Determining Sample Sizes
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 7 - Estimating Parameters and Determining Sample SizesProblem 7.3.3
Chapter 7, Problem 7.3.3

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.

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1
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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Introduction to Confidence Intervals

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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Fundamental Counting Principle

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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Related Practice
Textbook Question

Sample Size for Mean Find the sample size required to estimate the mean IQ of airline pilots. Assume that we want 99% confidence that the mean from the sample is within two IQ points of the true population mean. Also assume that sigma=15

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Textbook Question

Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.


Gender Selection Before its clinical trials were discontinued, the Genetics & IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl and, among the 945 babies born to parents using the XSORT method, there were 879 girls. The YSORT method was designed to increase the probability of conceiving a boy and, among the 291 babies born to parents using the YSORT method, there were 239 boys. Construct the two 95% confidence interval estimates of the percentages of success. Compare the results. What do you conclude?

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Textbook Question

FINDING SAMPLE SIZE Instead of using Table 7-2 for determining the sample size required to estimate a population standard deviation σ, the following formula can also be used


n=12(zα/2d)2n=\(\frac{1}{2}\]\left\)(\(\frac{z_{\alpha/2}\)}{d}\(\right\))^2


where zα/2z_{_{}\(\alpha\)/2} corresponds to the confidence level and d is the decimal form of the percentage error. For example, to be 95% confident that s is within 15% of the value of σ, use zα/2=1.96 and d=0.15 to get a sample size of n=86. Find the sample size required to estimate the standard deviation of IQ scores of data scientists, assuming that we want 98% confidence that s is within 5% of σ.

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Textbook Question

Constructing and Interpreting Confidence Intervals. In Exercises 13–16, use the given sample data and confidence level. In each case, (a) find the best point estimate of the population proportion p; (b) identify the value of the margin of error E; (c) construct the confidence interval; (d) write a statement that correctly interprets the confidence interval.


Eliquis The drug Eliquis (apixaban) is used to help prevent blood clots in certain patients. In clinical trials, among 5924 patients treated with Eliquis, 153 developed the adverse reaction of nausea (based on data from Bristol-Myers Squibb Co.). Construct a 99% confidence interval for the proportion of adverse reactions.

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Textbook Question

Job Interviews In a Harris poll of 514 human resource professionals, 463 said that the appearance of a job applicant is most important for a good first impression. Use 1000 bootstrap samples to construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that the appearance of a job applicant is most important for a good first impression. How does the result compare to the confidence interval found in Exercise 24 part (b) in Section 7-1?

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Textbook Question

Determining Sample Size. Assume that each sample is a simple random sample obtained from a normally distributed population.


You want to estimate for the population of diastolic blood pressures of air traffic controllers in the United States. Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 1% of σ. Is this sample size practical?

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