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Chapter 1: Problem 20

An engineer has just developed a new tire design. However, before going into production, the tire company wants to determine if the new tire reduces braking distance on a car traveling 60 miles per hour compared with radial tires. Design an experiment to help the engineer determine if the new tire reduces braking distance.

Short Answer

Expert verified
Conduct a controlled experiment comparing braking distances of cars with new tire design and radial tires using consistent test conditions.

Step by step solution

01

Define the Objective

Clearly state the objective of the experiment. In this case, the objective is to determine if the new tire design reduces braking distance compared to radial tires on a car traveling at 60 miles per hour.
02

Identify the Variables

Identify the independent and dependent variables. The independent variable is the type of tire (new tire design vs. radial tires). The dependent variable is the braking distance.
03

Formulate the Hypothesis

Formulate a testable hypothesis. For example: 'The new tire design reduces the braking distance compared to radial tires when a car is traveling at 60 miles per hour.'
04

Select a Sample

Choose an appropriate number of cars for the experiment to ensure reliability and accuracy. Randomly select cars of the same make and model to maintain consistency.
05

Conduct the Experiment

Test each car with both the new tire design and the radial tires. Ensure that the tests are conducted under the same conditions - same speed (60 miles per hour), same road surface, and similar weather conditions.
06

Measure and Record Data

Measure the braking distances for each car with both types of tires. Record the data systematically.
07

Analyze the Data

Use statistical methods to analyze the recorded data. Compare the average braking distances for the new tire design versus the radial tires.
08

Draw a Conclusion

Based on the data analysis, conclude whether the new tire design significantly reduces braking distance compared to radial tires.

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Key Concepts

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

dependent variables
In experimental design, identifying dependent variables is crucial. Dependent variables are the outcomes or responses that you measure in an experiment. They depend on or are influenced by other factors.
For example, in our tire study, the dependent variable is the braking distance. This is what changes when you switch from radial tires to the new tire design.
Understanding dependent variables helps in measuring the effect of the changes you make to your independent variables.
independent variables
Independent variables are the factors that you change or control in an experiment to observe their effects on dependent variables. They are the cause in a cause-and-effect relationship.
In our experiment, the independent variable is the type of tire used (new tire design vs. radial tires).
Choosing the right independent variables is critical to test your hypothesis properly.
hypothesis testing
Hypothesis testing involves making a prediction and then using statistical methods to determine if your data supports that prediction. This is a cornerstone of scientific experiments.
A typical hypothesis might be: 'The new tire design will reduce braking distance compared to radial tires.'
To test this hypothesis, you collect data and use statistical analyses to see if the observed results align with your prediction.
This helps you determine the probability that your hypothesis is true.
data analysis
Once you have collected your data, the next step is data analysis. This process involves using statistical methods to interpret your data.
For our tire experiment, you would calculate the average braking distances for both the new tire design and the radial tires.
Then, you could use statistical tests, like t-tests, to determine if the differences observed are statistically significant. This will help you understand if the new tire design truly reduces braking distance or if the results occurred by chance.
sample selection
Sample selection is about choosing the right participants or items to include in your experiment. A well-selected sample can improve the reliability and validity of your results.
For our experiment, you need to select cars. Ensure that the cars are of the same make and model to eliminate variables that could affect braking distance. This way, you can be confident that any observed differences in braking distance are due to the tire type and not other factors.
Random selection can also help ensure that your sample is representative of the larger population, which improves the generalizability of your results.

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Most popular questions from this chapter

The human resource department at a certain company wants to conduct a survey regarding worker morale. The department has an alphabetical list of all 4,502 employees at the company and wants to conduct a systematic sample. (a) Determine \(k\) if the sample size is \(50 .\) (b) Determine the individuals who will be administered the survey. More than one answer is possible.

Determine whether the quantitative variable is discrete or continuous. Number of donors at a blood drive

Researchers wanted to evaluate whether ginkgo, an over-the-counter herb marketed as enhancing memory, improves memory in elderly adults as measured by objective tests. To do this, they recruited 98 men and 132 women older than 60 years and in good health. Participants were randomly assigned to receive ginkgo, \(40 \mathrm{mg} 3\) times per day, or a matching placebo. The measure of memory improvement was determined by a standardized test of learning and memory. After 6 weeks of treatment, the data indicated that ginkgo did not increase performance on standard tests of learning, memory, attention, and concentration. These data suggest that, when taken following the manufacturer's instructions, ginkgo provides no measurable increase in memory or related cognitive function to adults with healthy cognitive function. (Source: "Ginkgo for Memory Enhancement," Paul R. Solomon, et. al.; Journal of the American Medical Association 288(2002): 835-840)$ (a) What type of experimental design is this? (b) What is the population being studied? (c) What is the response variable in this study? (d) What is the factor? What are the treatments? (e) Identify the experimental units. (f) Draw a diagram similar to Figure 6 or 7 to illustrate the design.

Research the placebo effect and the Hawthorne effect. Write a paragraph that describes how each affects the outcome of an experiment.

Identify the type of sampling used. A radio station asks its listeners to call in their opinion regarding the use of U.S. forces in peacekeeping missions.
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