In: Statistics and Probability
Here are the summary statistics for randomly selected weights of newborn girls: n=237, mean=33.8 hg, and s=6.2 hg. Construct a confidence interval estimate of the mean. Use a 90% confidence level
solution
Given that,
= 33.8
s =6.2
n = 237
Degrees of freedom = df = n - 1 =237 - 1 = 236
At 90% confidence level the t is ,
= 1 - 90% = 1 - 0.90 = 0.1
/ 2 = 0.1 / 2 = 0.05
t
/2,df = t0.05,236 = 1.651 ( using
student t table)
Margin of error = E = t/2,df
* (s /
n)
= 1.651* ( 6.2/
237) = 0.66
The 90% confidence interval is,
- E <
<
+ E
33.8-0.66 <
< 33.8+ 0.66
33.14 <
< 34.46
(33.14 , 34.46 )