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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 7.4.7b
Chapter 7, Problem 7.4.7b

7. FRESHMAN 15 Here is a sample of amounts of weight change (kg) of college students in their freshman year (from Data Set 13 “Freshman 15” in Appendix B): 11, 3, 0, –2, where –2 represents a loss of 2 kg and positive values represent weight gained. Here are ten bootstrap samples:
{11, 11, 11, 0}, {11, –2, 0, 11}, {11, –2, 3, 0}, {3, –2, 0, 11}, {0, 0, 0, 3}, {3, –2, 3, –2}, {11, 3, –2, 0}, {–2, 3, –2, 3}, {–2, 0, –2, 3}, {3, 11, 11, 11}.
b. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the standard deviation of the weight changes for the population.

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Step 1: Understand the problem. We are tasked with constructing an 80% confidence interval for the standard deviation of the weight changes in the population using the given bootstrap samples. Bootstrap sampling is a resampling method used to estimate the distribution of a statistic (e.g., standard deviation) by repeatedly sampling with replacement from the original data.
Step 2: Calculate the standard deviation for each of the ten bootstrap samples. The formula for standard deviation is: ∑(x-x¯)2)n, where x represents each data point, x̄ is the mean of the sample, and n is the number of data points in the sample.
Step 3: Once the standard deviations for all ten bootstrap samples are calculated, arrange them in ascending order. This will allow us to identify the range of values that correspond to the middle 80% of the distribution.
Step 4: To construct the 80% confidence interval, exclude the lowest 10% and the highest 10% of the standard deviation values. This means you will identify the 10th percentile and the 90th percentile of the sorted standard deviation values from the bootstrap samples.
Step 5: The 80% confidence interval for the standard deviation is then given by the range between the 10th percentile and the 90th percentile of the bootstrap standard deviation values. Interpret this interval as the range within which the true standard deviation of the population is likely to fall with 80% confidence.

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Key Concepts

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

Bootstrap Sampling

Bootstrap sampling is a resampling technique used to estimate the distribution of a statistic by repeatedly sampling with replacement from the original data set. This method allows for the creation of multiple simulated samples, which can help in estimating parameters like the mean or standard deviation, especially when the original sample size is small or when the underlying distribution is unknown.
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Sampling Distribution of Sample Proportion

Confidence Interval

A confidence interval is a range of values, derived from a data set, that is likely to contain the true population parameter with a specified level of confidence, such as 80%. It provides an estimate of uncertainty around a sample statistic, allowing researchers to understand the precision of their estimates and make inferences about the population from which the sample was drawn.
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Introduction to Confidence Intervals

Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It quantifies how much the individual data points deviate from the mean of the data set. In the context of the question, calculating the standard deviation of weight changes helps to understand the variability in weight gain or loss among college students during their freshman year.
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Calculating Standard Deviation
Related Practice
Textbook Question

Mean Pulse Rate of Females Data Set 1 “Body Data” in Appendix B includes pulse rates of 147 randomly selected adult females, and those pulse rates vary from a low of 36 bpm to a high of 104 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult females. Assume that we want 99% confidence that the sample mean is within 2 bpm of the population mean.


b. Assume that sigma=12.5 bpm, based on the value of s=12.5 bpm for the sample of 147 female pulse rates.


Textbook Question

Online Gambling Some states now allow online gambling. As a marketing manager for a casino, you need to determine the percentage of adults in those states who gamble online. How many adults must you survey in order to be 99% confident that your estimate is in error by no more than two percentage points?


b. Assume that 18% of all adults gamble online (based on 2017 data from a Gambling Commission study in Great Britain).

Textbook Question

Minting Quarters Listed below are weights (grams) of quarters minted after 1964 (based on Data Set 40 “Coin Weights” in Appendix B).


b. Specifications require that the quarters have a weight of 5.670 g. What does the confidence interval suggest about that specification?


Textbook Question

Comparing Waiting Lines


The values listed below are waiting times (in minutes) of customers at the Bank of Providence, where customers may enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation sigma.

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.


OxyContin The drug OxyContin (oxycodone) is used to treat pain, but it is dangerous because it is addictive and can be lethal. In clinical trials, 227 subjects were treated with OxyContin and 52 of them developed nausea (based on data from Purdue Pharma L.P.).


b. Compare the result from part (a) to this 95% confidence interval for 5 subjects who developed nausea among the 45 subjects given a placebo instead of OxyContin: . What do you conclude?

Textbook Question

Alcohol in Children’s Movies Listed below is a simple random sample of times (seconds) that animated children’s movies showed the use of alcohol (based on Data Set 20 “Alcohol and Tobacco in Movies” in Appendix B).


b. Are the requirements for constructing a 95% confidence interval estimate of the population standard deviation satisfied? If so, construct that confidence interval.