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=30 Mean x¯¯¯=103 Standard deviation s=12
Solution :
Given that,
= 103
s =12
n = 30
Degrees of freedom = df = n - 1 = 30- 1 = 29
a ) At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/
2= 0.05 / 2 = 0.025
t
/2,df = t0.025,29 = 2.045 ( using student t
table)
Margin of error = E = t/2,df
* (s /
n)
= 2.045 * ( 12/
30)
E= 4.4804
The 95% confidence interval estimate of the population mean is,
- E <
<
+ E
103- 4.4804 <
< 103+ 4.4804
98.5196 <
< 107.4804
( 98.5196,107.4804 )
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