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

$$n=7$$

$$\bar{x}=7041.4$$

$$s=1610.3$$

$$C=99\mathrm{\%}$$

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

$$\bar{x}-t_{\alpha }\cdot \frac{s}{\sqrt{n}}\le \mu \le \bar{x}+t_{\alpha }\cdot \frac{s}{\sqrt{n}}$$

$$7041.4-(3.707)\cdot \left(\frac{1610.3}{\sqrt{7}}\right)\le \mu \le 7041.4+(3.707)\cdot \left(\frac{1610.3}{\sqrt{7}}\right)$$

$$4785.2\le \mu \le 9297.6$$