Question

In: Statistics and Probability

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=20

Mean x¯¯¯=104

Standard deviation s=14

<μ<

Expert Solution

Solution :

Given that,

= 104

s =14

n = Degrees of freedom = df = n - 1 = 20- 1 = 19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2= 0.05 / 2 = 0.025

t /2,df = t0.025,19 = 2.093 ( using student t table)

Margin of error = E = t/2,df * (s / $\sqrt$ n)

= 2.093* ( 14/ $\sqrt$ 20)

= 6.55

The 95% confidence interval mean is,

- E < < + E

104 - 6.55 < < 104+ 6.55

97.45 < < 110.55

orchestra answered 2 years ago

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