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 )