Find the Confidence Interval Specified $\begin{array} { l l l l l } 5.1 & 4.9 & 4.7 & 3.1 & 4.3 \end{array}$

question 78

Multiple Choice

Find the confidence interval specified.
-Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering From asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity,
In liters.
$\begin{array} { l l l l l } 5.1 & 4.9 & 4.7 & 3.1 & 4.3 \end{array}$
$\begin{array} { l l l l l l } 3.7 & 3.7 & 4.3 & 3.5 & 5.2 \end{array}$
$\begin{array} { l l l l l } 3.2 & 3.5 & 4.8 & 4.0 & 5.1 \end{array}$
Use the data to obtain a $95.44 \%$ confidence interval for the mean forced vital capacity for all asthmatics. Assume that $\sigma = 0.7$ .

• A)\(4.11\) to \(4.30\) liters
• B) \(62.74\) to \(63.46\) liters
• C) \(3.85\) to \(4.57\) liters
• D) \(2.81\) to \(5.61\) liters

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Definitions:

Statistical Reasoning

The process of using statistical techniques and methods to analyze data and make conclusions based on data analysis.

Deliberate System

A cognitive process characterized by the slow, logical, and conscious evaluation of information, contrasting with automatic, quick, and unconscious processing.

Automatic System

Processes in the brain that occur without conscious effort, often quickly and based on learned routines.

Statistical Reasoning

The process of using statistical methods and principles to analyze, interpret, and draw conclusions from data.