In this case, since the standard deviation is known and
the sample size is less than 30, we will use the t-distribution. The formula
for calculating the confidence interval is:
Confidence Interval = X ± t * s / sqrt(n)
Where,
X = sample mean = $664.14
t = t score (taken from standard distribution tables)
s = standard deviation = $297.29
n = sample size = 14
At Degrees of Freedom = n – 1 = 13 and 98% Confidence
interval, z = 2.65
Substituting the values in the equation:
Confidence Interval = 664.14 ± 2.65 * 297.29 / sqrt(14)
Confidence Interval = 664.14 ± 210.55
Confidence Interval = 453.59 to 874.69
<span>
ANSWER: <span>
$453.56
< CI < $874.72</span></span>