Use the given data to find the 95% confidence interval estimate of the population mean μ...

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< _____

Solutions

Expert Solution

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 / $\sqrt$ n)

= 2.064 * (15 / $\sqrt$ 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

orchestra answered 1 year ago

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