Question
In: Statistics and Probability
If X=66, S=27 and n=36, and assuming that the population is normally distributed, construct a 95...
If X=66, S=27 and n=36, and assuming that the population is normally distributed, construct a 95 % confidence interval estimate of the population mean.
Solutions
Expert Solution
Solution :
Given that,
= 66
s =27
n =36
Degrees of freedom = df = n - 1 =36 - 1 = 35
At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/
2= 0.05 / 2 = 0.025
t
/2,df = t0.025,35 = 2.030 ( using student t
table)
Margin of error = E = t/2,df
* (s /
= 2.030 * (27 /
= 9.1
The 95% confidence interval estimate of the population mean is,
- E < 
<
+ E
66-9.1 <
< 66+ 9.1
56.9 <
< 75.1
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