The 99% confidence interval for a sample of size n, with sample mean of [tex]\bar{x}[/tex] and a sample standard deviation of s is given by
[tex]99\% \ C.I.=\bar{x}\pm t_{(\alpha/2,\ k)} \frac{s}{\sqrt{n}} [/tex]
where k is the degree of freedom, given by sample size - 1 (n - 1) = 13 - 1 = 12.
From the t-table, [tex]t_{(0.005,\ 12)}=3.05454[/tex].
Thus, given that a
meteorologist who sampled 13 randomly selected thunderstorms found that
the average speed at which they traveled across a certain state was 15.0
miles per hour. the standard deviation of the sample was 1.7 mph.
The 99% confidence interval of the mean is given by
[tex]99\% \ C.I.=15.0\pm 3.05454\times \frac{1.7}{\sqrt{13}} \\ \\ =15.0\pm3.05454\times\frac{1.7}{3.60555}=15.0\pm3.05454\times0.47150 \\ \\ =15.0\pm1.4402=\bold{(13.6,\ 16.4)}[/tex]
