/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 \- Arm length How long is your a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 29

\- Arm length How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. Repeat this a third time. Now your little finger will probably have reached the back of your left hand. If the fourth hand width goes past the end of your middle finger, turn your hand sideways and count finger widths to get there. a) How many hand and finger widths is your arm? b) Suppose you repeat your measurement 10 times and average your results. What parameter would this average estimate? What is the population? c) Suppose you now collect arm lengths measured in this way from 9 friends and average these 10 measurements. What is the population now? What parameter would this average estimate? d) Do you think these 10 arm lengths are likely to be representative of the population of arm lengths in your community? In the country? Why or why not?

Short Answer

Expert verified
a) Count hand units. b) True average of one person's measurement. c) True average among the group. d) Unlikely to represent larger populations accurately.

Step by step solution

01

Measure Hand Units

Start by measuring how many hand widths fit along the length of your arm. Place your right thumb at your left shoulder, stretch your hand open wide, and mark your little finger on the arm. Move your thumb to this mark and repeat until you cover the entire length of your arm. Count the hand widths and note partial measurements using finger widths if necessary.
02

Understanding Parameter and Population

When you repeat the measurement 10 times and average the results, you're estimating the 'true' average hand-unit length of your arm. The population in this context refers to the concept that would include all possible hand unit measurements you could perform.
03

Expanding to a Group

Now, if you collect similar measurements from 9 friends and average these 10 arm-lengths, the population describes the group of all possible arm lengths that could be measured using the hand method in your social circle. The average would estimate the 'true' hand-unit arm length for this group.
04

Evaluating Representativeness

The 10 arm lengths measured (yours and nine friends) may not represent the community or country's population due to sample size and diversity limitations. There might not be enough variation in the sample to reflect the broader population's arm lengths accurately due to geographic, genetic, and lifestyle differences.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Measurement Techniques
When measuring your arm length using your hand, you're engaging in a simple yet effective measurement technique. Unlike tools like rulers or measuring tapes, this method relies on the consistency of using the same hand as a unit of measure. This ensures a certain level of uniformity when conducting the measure.

To perform this method, extend your hand as widely as possible and use it to measure from your shoulder down your arm. Mark each hand's breadth with your thumb as a reference point and repeat until you've covered the full arm length.

If you reach the end of your arm and need additional precision, measure the remaining length using the width of your fingers to complete any partial measure. This mix of hand and finger measurements forms a practical way to gauge arm length without specialized tools. It serves as a straightforward introduction to understanding sizes and lengths through an intuitive and hands-on approach.
Population and Sample
In statistical terms, a population refers to the entire group you want to draw conclusions about, while a sample is a subset of this group.

Initially, when you measure your arm length multiple times and average the results, your population consists of all possible measurements of your arm. However, as you average multiple measurements, you approximate the 'true' average measurement of your own arm.

When you gather measurements from your friends and average these with your measurements, the definition of the population shifts. Now, the population may include all possible arm lengths within your social circle that could be measured using the hand unit method.

Here, your group of friends acts as a sample when trying to estimate an average arm length that might represent a larger population, like your community.
Representativeness
Representativeness is a crucial concept in statistical estimation and refers to how well a sample reflects the population from which it is drawn. A representative sample should have key characteristics that closely mirror those of the larger population.

In this exercise, measuring the arm lengths of your friends provides a sample that might not be fully representative of a larger population.
  • Sample Size: With only 10 arm lengths, the sample size is limited, which might not capture the full diversity of arm lengths present in a broader community or country.
  • Diversity: Your sample may lack diversity due to all participants being from a similar social group or geographic area, which could influence the range of arm lengths measured.
Thus, while your sample can provide an estimate, it might not fully capture the variability present in a larger population.
Estimation of Parameters
Estimating parameters is about using data from a sample to draw conclusions about the population. In this context, a parameter is a numerical value summarizing a characteristic of the population, such as the average arm length.

By averaging the hand unit arm lengths you collected, you aim to estimate the 'true' average arm length for your sample group. This estimation hinges on the assumption that your measurements represent a valid sample of the population you are interested in.

Estimating parameters requires understanding that individual measures, like each person's arm length, contribute to the variation seen in the sample. With more measures and a more diverse sample, your estimation of the population parameter generally improves. Tools like confidence intervals can quantify the uncertainty of your estimates, but the core idea is to use your data to make informed guesses about unknown population values.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

\- Accounting Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the transactions to be sure they were processed properly. a) Propose a sampling strategy for the supervisor. b) How would you modify that strategy if the company makes both wholesale and retail sales, requiring different bookkeeping procedures?

\- Happy workers? A manufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month. a) Do you see any potential danger in the company's plan? Explain. b) Propose a sampling strategy that uses a simple random sample. c) Why do you think a simple random sample might not provide the representative opinion the company seeks? d) Propose a better sampling strategy. e) Listed below are the last names of the project managers. Use random numbers to select two people to be interviewed. Explain your method carefully. \(\begin{array}{lll}\text { Barrett } & \text { Bowman } & \text { Chen } \\\ \text { Delara } & \text { DeRoos } & \text { Grigorov } \\ \text { Maceli } & \text { Mulvaney } & \text { Pagliarulo } \\ \text { Rosica } & \text { Smithson } & \text { Tadros } \\ \text { Williams } & \text { Yamamoto }\end{array}\)

Drug tests Major League Baseball tests players to see whether they are using performance-enhancing drugs. Officials select a team at random, and a drug- testing crew shows up unannounced to test all 40 players on the team. Each testing day can be considered a study of drug use in Major League Baseball. a) What kind of sample is this? b) Is that choice appropriate?

Phone surveys Anytime we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and \(4 \mathrm{PM}\), and interview whoever answers, anticipating contacts with at least 200 people. a) Why is it difficult to use a simple random sample here? b) Describe a more convenient, but still random, sampling strategy. c) What kinds of households are likely to be included in the eventual sample of opinion? Excluded? d) Suppose, instead, that we continue calling each number, perhaps in the morning or evening, until an adult is contacted and interviewed. How does this improve the sampling design? e) Random-digit dialing machines can generate the phone calls for us. How would this improve our design? Is anyone still excluded?

Texas A \& M Administrators at Texas A\&M University were interested in estimating the percentage of students who are the first in their family to go to college. The A\&M student body has about 46,000 members. a) What problems do you see with asking the following question of students? "Are you the first member of your family to seck higher education?" b) For each scenario, identify the kind of sample used by the university administrators: i. Select several dormitories at random and contact everyone living in the selected dorms. ii. Using a computer-based list of registered students, contact 200 freshmen, 200 sophomores, 200 juniors, and 200 seniors selected at random from each class. iii. Using a computer-based alphabetical list of registered students, select one of the first 25 on the list by random and then contact the student whose name is 50 names later, and then every 50 names beyond that. c) A professor teaching a large lecture class of 350 students samples her class by rolling a die. Then, starting with the row number on the die (1 to 6), she passes out a survey to every fourth row of the large lecture hall. She says that this is a Simple Random Sample because everyone had an equal opportunity to sit in any seat and because she randomized the choice of rows. What do you think? Be specific. d) For each of these proposed survey designs, identify the problem and the effect it would have on the estimate of the percentage of students who are the first in their family to go to college. i. Publish an advertisement inviting students to visit a website and answer questions. ii. Set up a table in the student union and ask students to stop and answer a survey. e) The president of the university plans a speech to an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend college, but the first draft of his speech treats that proportion as the actual proportion of current A\&M students who are the first in their families to attend college. Explain to the president the difference between the proportion of respondents who are first attenders and the proportion of the entire student body that are first attenders. Use appropriate statistics terminology.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.