/*! 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 Shoes A running-shoe manufacture... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 29

Shoes A running-shoe manufacturer wants to test the effect of its new sprinting shoe on 100 -meter dash times. The company sponsors 5 athletes who will try out for the 100 -meter dash in the 2016 Summer Olympic games. To test the shoe, it has all 5 runners run the 100 -meter dash with a competitor's shoe and then again with their new shoe. The company uses the difference in times as the response variable. a) Suggest some improvements to the design. b) Why might the shoe manufacturer not be able to generalize the results they find to all runners?

Short Answer

Expert verified
Increase sample size and randomization to improve the study. Results may not generalize due to a small, specific sample.

Step by step solution

01

Identify the Current Study Design

The study involves 5 athletes running a 100-meter dash twice, once with a competitor's shoe and once with the new shoe, measuring the difference in time as the response variable.
02

Suggesting Improvements for Study Design

Firstly, increase the sample size to include a more diverse group of athletes to minimize variability caused by individual differences. Secondly, use a double-blind test to prevent bias from knowledge of which shoes are being worn at any time. Furthermore, randomize the order in which the shoes are tested for each athlete to prevent any learning or fatigue effects.
03

Addressing the Issue of Sample Size

A larger sample size can provide more reliable, generalizable data. It reduces the influence of outliers or individual variability on the results. Therefore, including more athletes will help ensure that the findings reflect average performance enhancements attributable to the new shoe.
04

Explanation of Lack of Generalization

The study uses a very small, specific sample size, which may not represent the performance of the entire population of runners. The athletes are also training for the Olympics, indicating they are not typical runners, which might produce different results than those observed in the general running population. Additionally, individual differences such as running style, weight, and foot shape could affect how effective the shoes are.
05

Conclusion Regarding Generalization

Without diverse and adequately sized sampling, the manufacturer cannot claim that the shoe improves performance for all runners. The results are specific to the individuals tested under specific conditions and thus may not extend to all scenarios.

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.

Sample Size
When conducting any study, especially in experimental designs like testing new products, the sample size plays a crucial role. It refers to the number of subjects participating in the study. In the exercise, only 5 athletes were involved, which is considered a small sample size. By increasing the sample size, the study's reliability and the validity of its conclusions improve significantly.

A larger sample size helps in several ways:
  • It averages out individual differences, which can reduce the impact of outliers that might skew results.
  • It provides a broader representation of the population, allowing results to be more generalizable.
  • It increases statistical power, which makes it easier to detect true effects of the new shoe.
Ultimately, expanding the sample size means including athletes with diverse backgrounds, characteristics, and running habitats to ensure a holistic understanding of the shoe鈥檚 performance.
Response Variable
In studies like this, identifying and measuring a response variable is crucial because it determines the outcome that researchers are interested in. Here, the response variable is the time difference achieved by the athletes when using the new shoe versus the competitor's shoe.

Understanding response variables can be simple yet powerful:
  • The response variable should clearly relate to the hypothesis being tested. In this case, it's whether the new shoe improves sprinting performance.
  • It's important to measure it under consistent and controlled conditions to ensure validity.
  • Analyzing this variable helps researchers to draw conclusions regarding the effect of the treatment, in this case, the shoe design.
Having a well-defined response variable is essential to obtaining clear, interpretable results that can indicate a true benefit of the new product being tested.
Bias Prevention
Bias is an ever-present risk in studies where the goal is to prove the efficacy of a new product. In this scenario, eliminating bias is as crucial as expanding the sample size. Bias can lead to misleading results and affect the study's credibility. Several steps were recommended to avoid bias:

  • Implementing a double-blind procedure where neither the athletes nor the facilitators know which shoe is being tested at any time reduces expectation influence.
  • Randomizing the order in which each athlete wears each shoe helps counteract any learning or fatigue effects that might occur from running multiple times.
  • Having unbiased observers or automated systems to record times ensures objective data collection.
Together, these strategies help create a more objective study environment, where the true influence of the new shoe is observed.
Generalization
Generalization refers to the likelihood that the results of a study can be applied to a wider population beyond the sample studied. In this context, the study on Olympic-level athletes is not easily generalizable to all runners, because:

  • Elite athletes often have different physiological and biomechanical characteristics that might not be typical of everyday runners.
  • The small, homogeneous sample size restricts the study鈥檚 ability to reflect diverse running techniques, body types, or shoe preferences.
  • Specific training or conditions applicable only to top-tier athletes might skew results compared to those experienced by the general population.
Studying a more varied group helps researchers understand how the shoe performs universally, allowing claims about its effectiveness to reach more potential users.

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

Insomnia again Exercises 10 and 22 describe an experiment investigating the effectiveness of exercise in combating insomnia. Researchers randomly assigned half of the 40 volunteers to an exercise program. a) Why was it important to randomize in deciding who would exercise? b) What would be the advantages and disadvantages of using 100 subjects instead of \(40 ?\)

Multiple sclerosis (MS) is an autoimmune disease that strikes more often the farther people live from the equator. Could vitamin D - which most people get from the sun's ultraviolet rays - be a factor? Researchers compared vitamin D levels in blood samples from 150 U.S. military personnel who have developed MS with blood samples of nearly 300 who have not. The samples were taken, on average, five years before the disease was diagnosed. Those with the highest blood vitamin D levels had a \(62 \%\) lower risk of MS than those with the lowest levels. (The link was only in whites, not in blacks or Hispanics.) a) What kind of study was this? b) Is that an appropriate choice for investigating this problem? Explain. c) Who were the subjects? d) What were the variables?

Reading Some schools teach reading using phonics (the sounds made by letters) and others using whole language (word recognition). Suppose a school district wants to know which method works better. Suggest a design for an appropriate experiment.

Full moon It's a common belief that people behave strangely when there's a full moon and that as a result police and emergency rooms are busier than usual. Design a way you could find out whether there is any merit to this belief. Will you use an observational study or an experiment? Why?

Tomatoes II The chapter also described a completely randomized two-factor experiment testing OptiGro fertilizer in conjunction with two different routines for watering the plants. Describe a strategy to randomly assign the 24 tomato plants to the six treatments.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.