Data from the National Fire Protection Association gives a sample f 7 homes with a sample mean 704.14 and a sample standard deviation f 1610.3. Find the 99% confidence interval for the mean number of home fires started by candles each year.

Step 1:

Collect all of the relevant information

\[n=7\]

\[\overline{x}=7041.4\]

\[s=1610.3\]

\[C=99\%\]

Step 2:

Find the degrees of freedom \(df=n-1\)

\[df=7-1=6\]

Step 3:

Find the \(t_{\alpha}\) value for confidence 99% and df=6 from the t-table

\[t_{\alpha}=3.707\]

Step 4: 

Plug into our formula

\[\overline{x}-t_{\alpha}\cdot\frac{s}{\sqrt{n}}\leq\mu\leq\overline{x}+t_{\alpha}\cdot\frac{s}{\sqrt{n}} \]

\[7041.4-(3.707)\cdot\left(\frac{1610.3}{\sqrt{7}}\right)\leq\mu\leq7041.4+(3.707)\cdot\left(\frac{1610.3}{\sqrt{7}}\right)\]

\[4785.2\leq\mu\leq9297.6\]