Answer:
[$489.83, $883.67]
Step-by-step explanation:
The 98% confidence interval is given by the interval
where
=686.75 is the sample mean
s = 256.20 is the sample standard deviation
n = 15 is the sample size
t is the 2% critical value for the Student's t-distribution with 14 degrees of freedom (sample size -1), this is a value such that the area under the Student's t curve outside the interval [-t, t] is 2%=0.02.
We are using the t-distribution for it is the approximation to the Normal distribution for small samples (n<30).
Either by using a table or the computer, we find
t = 2.9768
In Excel we use the function
<em>TINV(0.01,14) </em>
In OpenOffice Calc
<em>TINV(0.01;14) </em>
and our 98% confidence interval is