A normal resting heart rate for adults ranges from about 60 to 100 beats per minute (BPM). A doctor would like to estimate the average heart rate for one of her patients. The doctor instructs her patient to measure their resting heart rate twice a day for one week. The measurements are listed below. Assume that the distribution of all heart rate measurements of this patient is approximately normally distributed.
\begin{tabular}{|l|l|}
\hline 106 & 107 \\
\hline 113 & 100 \\
\hline 107 & 108 \\
\hline 111 & 107 \\
\hline 108 & 101 \\
\hline 112 & 112 \\
\hline 106 & 103 \\
\hline
\end{tabular}

Determine the point estimate, $\bar{x}$ and the sample standard deviation, $s$. Round the solutions to four decimal places, if necessary.
\[
\begin{array}{l}
\bar{x}= \\
s=
\end{array}
\]

Using an $80 \%$ confidence level, determine the margin of error, $E$, and a confidence interval for the average resting heart rate of this patient. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.

The margin of error is given by $E=$

An $80 \%$ confidence interval is given by

Step 1 ：Given the heart rate measurements of a patient over a week, we are asked to estimate the average heart rate and its standard deviation. The measurements are as follows: 106, 107, 113, 100, 107, 108, 111, 107, 108, 101, 112, 112, 106, 103.

Step 2 ：First, we calculate the point estimate, denoted as \( \bar{x} \), which is the sample mean of the measurements. The sample mean is calculated as the sum of all measurements divided by the number of measurements.

Step 3 ：Using the given measurements, the sample mean, \( \bar{x} \), is approximately 107.2143.

Step 4 ：Next, we calculate the sample standard deviation, denoted as \( s \). The sample standard deviation is a measure of the amount of variation or dispersion of the measurements.

Step 5 ：Using the given measurements, the sample standard deviation, \( s \), is approximately 3.9842.

Step 6 ：We are also asked to determine the margin of error and a confidence interval for the average resting heart rate of this patient at an 80% confidence level. The margin of error is calculated using the formula \( E = z \cdot s \), where \( z \) is the z-score corresponding to the desired confidence level and \( s \) is the sample standard deviation.

Step 7 ：The z-score for an 80% confidence level is approximately 1.2816. Therefore, the margin of error, \( E \), is approximately 5.11.

Step 8 ：Finally, we calculate the confidence interval, which is given by \( (\bar{x} - E, \bar{x} + E) \).

Step 9 ：The 80% confidence interval for the average resting heart rate of this patient is approximately (102.11, 112.32). Therefore, we can be 80% confident that the true average resting heart rate of this patient lies within this interval.

Step 10 ：In conclusion, the point estimate, \( \bar{x} \), is approximately \(\boxed{107.2143}\) and the sample standard deviation, \( s \), is approximately \(\boxed{3.9842}\). The margin of error, \( E \), is approximately \(\boxed{5.11}\). An 80% confidence interval for the average resting heart rate of this patient is approximately \(\boxed{(102.11, 112.32)}\).