Question
A simple random sample of 25 items from a normally distributed population resulted in a sample...
A simple random sample of 25 items from a normally distributed population resulted in a sample mean of 80 and a sample standard deviation of 7.5. Construct a 95% confidence interval for the population mean.
Homework Answers
Answer #1
Solution :
Given that,
= 80
s =7.5
n =25
Degrees of freedom = df = n - 1 = 25 - 1 = 24
At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/
2= 0.05 / 2 = 0.025
t
/2,df = t0.025,24 = 2.064 ( using student t
table)
Margin of error = E = t/2,df
* (s /
n)
=2.064 * (7.5 /
25)
= 3.096
The 95% confidence interval is,
- E < 
<
+ E
80 - 3.096 <
< 80+ 3.096
76.904 <
< 83.096
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