Question

Use the given data to find the 95% confidence interval estimate of the population mean u. Assume that the population has a normal distribution. IQ scores of professional athletes: Sample size n = 20 Mean x = 104 Standard deviation s = 9 <μ< Note: Round your answer to 2 decimal places.

Answer 1

Solution :

degrees of freedom = n - 1 = 20 - 1 = 19

t$\alpha$/2,df = t_0.025,19 = 2.093

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.093 * (9 / $\sqrt$ 20)

Margin of error = E = 4.21

The 95% confidence interval estimate of the population mean is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

104 - 4.21 < $\mu$ < 104 + 4.21

( 99.79 < $\mu$ < 108.21 )