A veterinarian investigating possible causes of enteroliths in horses suspects that feeding alfalfa may be to blame. she wishes to estimate the proportion of horses with enteroliths who are fed at least two flakes of alfalfa per day. in a sample of 62 horses with enteroliths, she finds 42 are fed two or more flakes of alfalfa. she estimates the standard error to be se = 0.0594. 0.2185. 0.0035. 0.4675.

The veterinarian wants to test if eating alfalfa causes enteroliths in horses. For that, she takes a random sample of horses with enteroliths and counts how many eat alfalfa. The study variable is X: Number of horses with enteroliths that eat alfalfa in a sample of 62 horses.

Binomial criteria:

1. The number of observations of the trial is fixed.

2. Each observation in the trial is independent, this means that none of the trials will have an effect on the probability of the next trial.

3. The probability of success in the same from one trial to another.

Since the variable meets the binomial criteria, you can say that it has a binomial distribution, symbolically X ~ Bi (n;p)

To estimate the proportion of horses that have enteroliths and eat alfalfa you have to make the following calculation:

[tex]p= \frac{x}{n} = \frac{42}{62} = 0.677[/tex] ≈ 0.68

This means that 68% of the horses with enteroliths eat alfalfa.

To calculate the standard error you need to calculate the variance and then its square root:

[tex]V(X)= np(1-p)= 62*0.68*0.32 = 13.4912[/tex]

[tex]\sqrt{V(X)} = \sqrt{13.4912} = 3.6730[/tex]

None of the given options corresponds to the standard error of the sample.

I hope it helps!