Question

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

Answer #1

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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