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A veterinarian collects data on the number of times race horses are raced during their careers. The veterinarian finds that the average number of races a horse enters is ????¯=15.3 , with a standard deviation of ????=6.8 in a sample of ????=20 horses. A 95% confidence for ???? , the average number of times a horse races, is ______.

1 Answer

1 vote

Answer:


[12.1175 , 18.4825]

Explanation:

An (
1-\alpha)% interval confidence for the population average, based on a sample of n individuals is given by:


[\hat x - T_(\alpha /2) \sqrt{(S^(2))/(n) }  , \hat x + T_(\alpha /2) \sqrt{(S^(2))/(n)} ], where
[\hat x is the sample means,
[ S^(2) is the sample standard deviation,
[T_(\alpha /2) is the quantile value of the distribution T with
(n-1) degrees of freedom and n is the sample size. thus,


[\hat x - T_(\alpha /2) \sqrt{(S^(2))/(n) }  , \hat x + T_(\alpha /2) \sqrt{(S^(2))/(n)} ] = [15.3 - 2.4334\sqrt{(46.24)/(20) } , 15.3 + 2.4334\sqrt{(46.24)/(20) } ] =[12.1175 , 18.4825]

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