Question

The article "More Communities Banning 'Television on a Stick"" (USA Today, March 23,2010 ) describes an ongoing controversy over the distraction caused by digital billboards along highways. One study mentioned in the newspaper article is described in "Effects of Advertising Billboards During Simulated Driving" (Applied Ergonomics [2010]: 1-8). In this study, 48 people made a \(9 \mathrm{~km}\) drive in a driving simulator. Drivers were instructed to change lanes according to roadside lane change signs. Some of the lane changes occurred near digital billboards. What was displayed on the digital billboard changed once during the time that the billboard was visible by the driver to simulate the changing digital billboards that appear along highways. Data from this study supported the theory that the time required to respond to road signs was greater when digital billboards were present. Is the inference made one that involves estimation or one that involves hypothesis testing? (Hint: See Example 7.1\()\)

Short answer

The inference made from the study involves hypothesis testing.

Step-by-step solution

Understanding the Difference Between Estimation and Hypothesis Testing

In statistics, estimation is the process where sample data is used to estimate an unknown population parameter. On the other hand, hypothesis testing is a method that uses sample data to test an assumption about the properties of a population. The main difference between the two is that while estimation provides a specific value (for instance, mean or standard deviation), hypothesis testing is done to either accept or reject an assumption.

Apply the Understanding to the Given Study

In the given study, the response times were greater when digital billboards were present. This statement supported a theory, it tested an assumption about the effect of digital billboards on response time. Therefore, this seems to be a case of testing a theory (or assumption) with the collected data.

Conclusion

From the properties of the statistical methods, it can be inferred that the conclusion made from the study was based on hypothesis testing. The collected data was used to test the theory that digital billboards increase the response time required for drivers to react to road signs.

Key concepts

Statistical Inference

Statistical inference is a critical concept in conducting research and analyzing data. It involves drawing conclusions about a population based on sample data. This process is fundamental in scientific studies, surveys, and experiments where it is impractical or impossible to observe every individual in the target group.

In the context of the driving simulation study, statistical inference is applied to draw conclusions about the general effect of digital billboards on drivers' response times to road signs. Researchers observed a sample (48 people) and collected data on their response times. Using this sample, statistical inference allows them to generalize the findings to a larger population of drivers, assuming that the sample accurately represents the entire group.

The two main types of statistical inference are estimation and hypothesis testing. Estimation would consist of calculating an estimate of the average increase in response time due to digital billboards, while hypothesis testing would involve assessing whether the digital billboards have a statistically significant effect on response time.

Estimation in Statistics

Estimation in statistics involves deriving the most plausible value of a population parameter based on sample data. These parameters could be the mean, proportion, variance, or standard deviation.

There are two types of estimators commonly used: point estimators and interval estimators. A point estimator provides a single value that best estimates the parameter, whereas an interval estimator provides a range of values, often with a specific confidence level, suggesting where the parameter lies.

For example, in the digital billboard study, if researchers wanted to estimate the average increase in response time, they would use the sample data to calculate a point estimate, like the sample mean response time. An interval estimate could then provide a confidence interval around the mean, signaling the researchers' confidence in the estimate.

Applied Ergonomics

Applied ergonomics is the science of designing and arranging things people use so that the people and things interact most efficiently and safely, which is particularly relevant in workplace and product design. It's essential in ensuring that systems are developed that complement the strengths and abilities of people while minimizing the effects of their limitations.

In the case of the driving simulator study, applied ergonomics would focus on understanding how digital billboards as part of the roadside environment may affect driver behavior and safety. The goal is not just to measure the distraction caused but to suggest design improvements to digital billboards or driver warning systems that reduce the risk without sacrificing the advertising benefits of digital billboards.

Sample Data Analysis

Sample data analysis is the examination of a subset of a larger population to understand and make inferences about the larger group as a whole. In many studies, such as in the context of the digital billboard research, it is not feasible to collect data from every member of a population.

Analysts therefore collect data from a representative sample and use statistical methods to analyze this data. Descriptive statistics describe the sample with measures such as mean and standard deviation, while inferential statistics allow us to generalize findings from our sample to the larger population with a certain degree of confidence. This process is foundational in the scientific method and helps guide decision-making in a broad range of fields, from medicine to public policy.