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In: Statistics and Probability

A random sample of 30 marathon runners demonstrated that the average age was 38 years old,...

A random sample of 30 marathon runners demonstrated that the average age was 38 years old, with s = 5 years. Find a 95% confidence interval for the average age of marathon runners.

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Expert Solution

solution

Given that,

= 38

s =5

n = 30

Degrees of freedom = df = n - 1 =30 - 1 =29

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 * (5 / 30) = 1.8668

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

- E < < + E

38 - 1.8668 < < 38+ 1.8668

36.1332 < < 39.8668

( 36.1332 , 39.8668)

orchestra answered 2 years ago
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