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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 7.3.16a
Chapter 7, Problem 7.3.16a

Comparing Waiting Lines


The values listed below are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows. Construct a 95% confidence interval for the population standard deviation sigma.
Waiting times in minutes: 6.5, 6.6, 6.7, 6.8, 7.1, 7.3, 7.4, 7.7, 7.7, 7.7.

Verified step by step guidance
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Step 1: Calculate the sample standard deviation (s) using the formula: s = sqrt((Σ(x_i - x̄)^2) / (n - 1)), where x_i represents each data point, x̄ is the sample mean, and n is the sample size.
Step 2: Determine the sample size (n) from the given data. In this case, count the number of waiting times provided.
Step 3: Use the Chi-Square distribution to construct the confidence interval for the population standard deviation (σ). The formula for the confidence interval is: CI = [sqrt((n - 1)s^2 / χ²_upper), sqrt((n - 1)s^2 / χ²_lower)], where χ²_upper and χ²_lower are the critical values from the Chi-Square table corresponding to the desired confidence level and degrees of freedom (df = n - 1).
Step 4: Look up the critical values χ²_upper and χ²_lower for a 95% confidence level and degrees of freedom (df = n - 1) in the Chi-Square distribution table.
Step 5: Plug the calculated sample standard deviation (s), sample size (n), and critical values (χ²_upper and χ²_lower) into the confidence interval formula to find the range for the population standard deviation (σ).

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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 population parameter with a specified level of confidence, typically 95%. It provides an estimate of uncertainty around a sample statistic, allowing researchers to infer 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. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. It is crucial for understanding the distribution of data and calculating confidence intervals.
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Chi-Square Distribution

The chi-square distribution is a statistical distribution that is used to estimate the variance of a population based on sample data. It is particularly relevant when constructing confidence intervals for the population standard deviation, as it allows for the determination of critical values needed for the calculations based on the sample size and desired confidence level.
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Related Practice
Textbook Question

E-Cigarettes A New York Times article reported that a survey conducted in 2014 included 36,000 adults, with 3.7% of them being regular users of e-cigarettes. Because e-cigarette use is relatively new, there is a need to obtain today’s usage rate. How many adults must be surveyed now if we want a confidence level of 95% and a margin of error of 1.5 percentage points?


a. Assume that nothing is known about the rate of e-cigarette usage among adults.

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Textbook Question

Analysis of Last Digits Weights of respondents were recorded as part of the California Health Interview Survey. The last digits of weights from 50 randomly selected respondents are listed below.



a. Use the bootstrap method with 1000 bootstrap samples to find a 95% confidence interval estimate of .

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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.


Tennis Challenges In a recent U. S. Open tennis tournament, women playing singles matches used challenges on 137 calls made by the line judges. Among those challenges, 33 were found to be successful with the call overturned.


a. Construct a 99% confidence interval for the percentage of successful challenges.

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Textbook Question

Cell Phone Radiation Here is a sample of measured radiation emissions (cW/kg) for cell phones (based on data from the Environmental Working Group): 38, 55, 86, 145. Here are ten bootstrap samples:

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a. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the population mean.


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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

Archeology Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures. Listed below are the widths (mm) of skulls from 150 A.D. (based on data from Ancient Races of the Thebaid by Thomson and Randall-Maciver).


a. Use 1000 bootstrap samples to construct a 99% confidence interval estimate of the mean skull width.


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