Question

A meteorologist who sampled 13 randomly selected thunderstorms found that the average speed at which they traveled across a certain state was 1.7 miles per hour. the standard deviation of the sample was 1.7 mph. find the 99% confidence interval of the mean. do not round the t value from the table

Answer 1

The 99% confidence interval for a sample of size n, with sample mean of
`\bar{x}` and a sample standard deviation of s is given by


`99\% \ C.I.=\bar{x}\pm t_((\alpha/2,\ k)) (s)/(√(n))`

where k is the degree of freedom, given by sample size - 1 (n - 1) = 13 - 1 = 12.

From the t-table,
`t_((0.005,\ 12))=3.05454`.

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


`99\% \ C.I.=15.0\pm 3.05454* (1.7)/(√(13)) \\ \\ =15.0\pm3.05454*(1.7)/(3.60555)=15.0\pm3.05454*0.47150 \\ \\ =15.0\pm1.4402=\bold{(13.6,\ 16.4)}`