In: Statistics and Probability
Use the given data to find the 95% confidence interval estimate of the population mean μ . Assume that the population has a normal distribution.
IQ scores of professional athletes:
Sample size n=25
Mean=103
Standard deviation s=15
Answer: ____ <μ< _____
Solution :
Given that,
= 103
s =15
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 * (15 /
25)
= 6.19
The 95% confidence interval estimate of the population mean is,
- E <
<
+ E
103 - 6.19 <
<103 + 6.19
96.81 <
< 109.19