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Chapter 5: Problem 26

The data given in Example \(5.5\) on \(x=\) call-to-shock time (in minutes) and \(y=\) survival rate (percent) were used to compute the equation of the least- squares line, which was $$ \hat{y}=101.36-9.30 x $$ The newspaper article "FDA OKs Use of Home Defibrillators" (San Luis Obispo Tribune, November 13,2002 ) reported that "every minute spent waiting for paramedics to arrive with a defibrillator lowers the chance of survival by 10 percent." Is this statement consistent with the given least-squares line? Explain.

Short Answer

Expert verified
The newspaper's statement is close but slightly overstates the decrease in survival time according to the least-squares line. The line suggests a 9.3% decrease per minute, whereas the statement claims a 10% decrease.

Step by step solution

01

Identify the slope

The slope of the least-squares line, represented by 'b' in the equation \(y = mx + b\), is -9.30. This slope shows the change in survival rate for each additional minute without a defibrillator. Negative slope indicates that survival rate decreases as time increases.
02

Translate the slope into a percentage

The slope of -9.30 means that for each additional minute spent waiting for a defibrillator, the survival rate goes down by 9.3 percent. This is due to the fact that the survival rate y is given in percentage.
03

Compare the statement and slope percentage

The newspaper statement says every minute waiting for a defibrillator lowers survival chance by 10 percent. Comparing this with the slope percentage of 9.3 percent, it can be seen that the statement is close but slightly overstates the decrease in survival rate according to the least-squares line.

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Key Concepts

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

Call-to-Shock Time
Call-to-shock time refers to the duration between a person experiencing a sudden cardiac arrest and the moment they receive treatment with a defibrillator. This period is crucial because the survival rate of a person suffering from cardiac arrest significantly decreases as time progresses without treatment.

Understanding the impact of call-to-shock time on survival is important for both medical professionals and policymakers, as it can inform the allocation of resources and the development of response protocols. The faster the response time, the higher the likelihood of survival, which is why many public spaces are now equipped with automated external defibrillators (AEDs) for emergency use.
Survival Rate
Survival rate in the context of medical emergencies like cardiac arrest refers to the percentage of people who survive after the event. It's a critical indicator of the effectiveness of emergency response systems and treatments, such as the use of defibrillators.

Factors affecting the survival rate include the immediate recognition of cardiac arrest, the speed at which cardiopulmonary resuscitation (CPR) is initiated, and the promptness of defibrillation. The statistical relationship between survival rate and call-to-shock time can provide valuable insights into areas for improvement in emergency medical services.
Statistical Analysis
Statistical analysis involves collecting, analyzing, and interpreting data to uncover patterns and relationships. In medical studies, such as those examining survival rates, statistical analysis can help to establish the effectiveness of interventions and identify factors that significantly impact outcomes.

In the case of call-to-shock time and survival rate, statistical analysis quantifies how changes in one variable (time) are associated with changes in the other variable (survival rate). Tools such as regression analysis allow researchers to make predictions and provide evidence-based recommendations for practice.
Regression Analysis
Regression analysis is a statistical method used to examine the relationship between a dependent variable and one or more independent variables. In the context of the call-to-shock time problem, regression analysis creates a model鈥攕uch as the least-squares line鈥攖o predict the survival rate (dependent variable) based on call-to-shock time (independent variable).

The equation of the least-squares line, \(\hat{y}=101.36-9.30x\), encapsulates this prediction. The negative slope of the line indicates that, as call-to-shock time increases, the expected survival rate decreases. Hence, the analysis confirms the critical importance of minimizing call-to-shock time to improve survival outcomes for cardiac arrest patients.

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Most popular questions from this chapter

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