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

Question

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

Quizplus · Accepted Answer

The confidence interval is calculated using the formula for a confidence interval when the population standard deviation ($\sigma$) is known, which is $\bar{x} \pm Z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level (for $95.44\%$ confidence level, $Z$ is approximately 2 since it's close to a 95% confidence interval which uses 1.96), $\sigma$ is the population standard deviation, and $n$ is the sample size. Calculating the sample mean from the given data and applying the formula with $\sigma = 0.7$ and $n = 15$, the interval that matches the calculation process is option C, $3.85$ to $4.57$ liters.

Find the Confidence Interval Specified 5.14.94.73.14.3\begin{array} { l l l l l } 5.1 & 4.9 & 4.7 & 3.1 & 4.3 \end{array}5.1​4.9​4.7​3.1​4.3​

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