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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 7.4.17a
Chapter 7, Problem 7.4.17a

Brain Volumes Use these measures of brain volumes from Data Set 12 “IQ and Brain Size” in Appendix B. Use the bootstrap method with 1000 bootstrap samples.


"Brain volume data set with values ranging from 963 to 1439 for statistical analysis."


a. Use 1000 bootstrap samples to construct a 90% confidence interval estimate of the population mean.

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Step 1: Understand the bootstrap method. The bootstrap method involves resampling the original dataset with replacement to create multiple simulated samples. These samples are used to estimate the sampling distribution of a statistic, such as the mean.
Step 2: Generate 1000 bootstrap samples. Randomly select values from the given dataset with replacement to create 1000 new samples, each of the same size as the original dataset.
Step 3: Calculate the mean for each bootstrap sample. For each of the 1000 bootstrap samples, compute the sample mean. This will give you a distribution of 1000 sample means.
Step 4: Determine the 90% confidence interval. Sort the 1000 bootstrap sample means in ascending order. Identify the 5th percentile and the 95th percentile of the sorted means. These values represent the lower and upper bounds of the 90% confidence interval for the population mean.
Step 5: Interpret the confidence interval. The 90% confidence interval provides a range within which the true population mean is likely to fall, with 90% confidence. This interval is based on the variability observed in the bootstrap samples.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Bootstrap Method

The bootstrap method is a resampling technique used to estimate the distribution of a statistic by repeatedly sampling with replacement from the observed data. This approach allows for the estimation of confidence intervals and standard errors without relying on strong parametric assumptions. In this case, it involves creating 1000 bootstrap samples from the brain volume data to assess the variability and construct a confidence interval for the population mean.
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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, such as 90%. It provides an estimate of uncertainty around the sample mean. For the brain volume data, constructing a 90% confidence interval means that if we were to take many samples and build intervals, approximately 90% of those intervals would contain the true mean brain volume.
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Population Mean

The population mean is the average of a set of values for an entire population, as opposed to a sample mean, which is calculated from a subset of the population. In the context of the brain volume data, the population mean represents the average brain volume across all individuals in the population being studied. Estimating this mean accurately is crucial for understanding the relationship between brain size and other variables, such as IQ.
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Related Practice
Textbook Question

Controversial Song The song “Baby It’s Cold Outside” generated much controversy because of its lyrics and tone. CBS New York conducted a survey by asking viewers to use the Internet to respond to a question asking whether that song was really too offensive to play. Among 1043 Internet users who chose to respond, 986 said that the song was not too offensive, and 57 of the respondents said that the song was too offensive.


a. Construct a 95% confidence interval estimate of the proportion of the population having the belief that the song is not too offensive.


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Textbook Question

Voting Survey In a survey of 1002 people, 70% said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote.


a. Among the 1002 people surveyed, what is the actual number of people who said that they voted?


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Textbook Question

Airline Seating You are the operations manager for American Airlines and you are considering a higher fare level for passengers in aisle seats. You want to estimate the percentage of passengers who now prefer aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 95% confident that the sample percentage is within 2.5 percentage points of the true population percentage.


a. Assume that nothing is known about the percentage of passengers who prefer aisle seats.


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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.


Touch Therapy When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily’s hand without seeing it and without touching it. Among 280 trials, the touch therapists were correct 123 times (based on data in “A Close Look at Therapeutic Touch,” Journal of the American Medical Association, Vol. 279, No. 13).


a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?

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Textbook Question

Astrology A sociologist plans to conduct a survey to estimate the percentage of adults who believe in astrology. How many people must be surveyed if we want a confidence level of 99% and a margin of error of four percentage points?


a. Assume that nothing is known about the percentage to be estimated.


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Textbook Question

Mean Pulse Rate of Males Data Set 1 “Body Data” in Appendix B includes pulse rates of 153 randomly selected adult males, and those pulse rates vary from a low of 40 bpm to a high of 104 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 99% confidence that the sample mean is within 2 bpm of the population mean.


a. Find the sample size using the range rule of thumb to estimate .


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