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

Answer:

$[12.1175 , 18.4825]$

Step-by-step explanation:

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

$[\hat x - T_{\alpha /2} \sqrt{\frac{S^{2}}{n} } , \hat x + T_{\alpha /2} \sqrt{\frac{S^{2}}{n}} ]$, 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,

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