Question

A veterinarian does research on the causes of enteroliths, stones that develop in the colon of horses. She suspects that feeding alfalfa might be a cause. To investigate that suspicion, she selects five horses that are known to have enteroliths and compares the number of flakes of alfalfa they have eaten over a month with the number of flakes eaten by five horses free of enteroliths. If she calculates a two-sample confidence interval by hand for the difference in the mean number of flakes fed to horses with and without enteroliths the degrees of freedom she should use are:

10.
8.
4.
5.

Answer 1

Answer: 8

Step-by-step explanation:

The degree of freedom for t-distribution of testing the differnce between the two population mean is given by :-

$df= n_1+n_2-2$

, where $n_1$ = Size of first sample.

$n_1$ = Size of second sample.

As per given ,

Veterinarian selects five horses that are known to have enteroliths and compares the number of flakes of alfalfa they have eaten over a month with the number of flakes eaten by five horses free of enteroliths.

i.e. $n_1=5$ and $n_2=5$

Now , If she calculates a two-sample confidence interval by hand for the difference in the mean number of flakes fed to horses with and without enteroliths the degrees of freedom she should use are

$df= 5+5-2=8$

Hence, the correct answer is 8.