In: Statistics and Probability
Assuming the population has an approximate normal distribution,
if a sample size n=10 has a sample mean ¯x=36 with a sample
standard deviation s=9, find the margin of error at a 90%
confidence level. THEN YOU MUST ROUND ANSWER TO TWO DECIMALS
PLACES.
Solution :
Given that,
t
/2,df = 1.833
Margin of error = E = t/2,df
* (s /
n)
= 1.833 * (9 /
10)
Margin of error = E = 5.22
The 90% confidence interval estimate of the population mean is,
- E <
<
+ E
36 - 5.22 <
< 36 + 5.22
30.78 <
< 41.22
(30.78 , 41.22)