Question

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 ______.

Answer 1

`[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]`