Answer:
![[12.1175 , 18.4825]](https://img.qammunity.org/2020/formulas/mathematics/college/f4kqghmm2mx3eyj3kmz8z82wjm0rx4yk5q.png)
Explanation:
An (
)% interval confidence for the population average, based on a sample of n individuals is given by:
, where
is the sample means,
is the sample standard deviation,
is the quantile value of the distribution T with
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]](https://img.qammunity.org/2020/formulas/mathematics/college/4idjh1a8tpox2kq7ijqlastkm0ow32b9a2.png)