In: Statistics and Probability
A random small sample of 15 novels making a national best seller
list was selected. The average length of time these novels stayed
on the best seller list was 5.2 weeks with standard deviation 2.3
weeks. Find the 99% confidence interval for the average number of
weeks a book is on the best seller list
Solution :
Given that,
Point estimate = sample mean =
= 5.2
sample standard deviation = s = 2.3
sample size = n = 15
Degrees of freedom = df = n - 1 = 15 - 1 = 14
At 99% confidence level the t is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
t
/2,df = t0.005,14 = 2.977
Margin of error = E = t/2,df
* (s /
n)
= 2.977 * (2.3 /
15)
= 1.8
The 99% confidence interval estimate of the population mean is,
- E <
<
+ E
5.2 - 1.8 <
< 5.2 + 1.8
3.4 <
< 7.0
(3.4 , 7.0)