Question
In: Statistics and Probability
if X=65, S=12, and n=16, and assuming that the population is normally distributed, construct a 90%...
if X=65, S=12, and n=16, and assuming that the population is normally distributed, construct a 90% confidence interval estimate of the population mean,μ
Solutions
Expert Solution
Solution :
Given that,
= 65
s = 12
n = 16
Degrees of freedom = df = n - 1 = 16 - 1 = 15
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
t
/2,df = t0.05,15 =1.753
Margin of error = E = t/2,df
* (s /
=1.753 * (12 /
= 5.26
Margin of error = 5.26
The 90% confidence interval estimate of the population mean is,
- E < 
<
+ E
65 - 5.26 <
< 65 + 5.26
59.74 <
< 70.26
(59.74, 70.26 )
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