Question

on a farm with 300 chickens, the birds are fed either organic feed (certified) or generic brand feed and lay eggs that are characterized as being extra-large, large, or small.

XL L S not organic feed | 25 125 30 organic feed 50 50 20

i) calculate the relative risk for the trait "lays extra-large eggs" with risk factor "is fed organic feed"

ii) are the following events independent, dependent, or mutually exclusive:

a) "lays extra-large eggs" and "is not fed organic feed"

b) "is organic fed" and "is not organic fed"

c) "lays large eggs" and "lays small eggs"

Answer 1

A B C D E 1 XL L S 25 125 2 not organic feed 3 Organic Feed 4 Total 30 20 Total 180 120 300 50 50 75 175 50 5 0.625 62.50% 6 i) Relative risk = 7 B4/E3

ii) a mutually exclusive event can simply be defined as a situation when two events cannot occur at same time.

Independent event occurs when one event remains unaffected by the occurrence of the other event.

Dependent event occurs when one event affects the occurrence of the other event.

If A and B are independent then $P(A \cap B)=P(A)P(B)$

If A and B are mutually exclusive then $P(A \cap B) =0$

a) probability "lays extra-large eggs" and "is not fed organic feed" is

$\frac{25}{300}=0.0833$

probability "lays extra-large eggs" = $\frac{75}{300}$

probability "is not fed organic feed" =$\frac{180}{300}$

$(\frac{75}{300})\frac{180}{300}=0.15$

Hence $P(A \cap B) \neq P(A)P(B)$ Thus these events are dependent events

b) "is organic fed" and "is not organic fed". These are mutually exclusive events

c) "lays large eggs" and "lays small eggs". These events are mutually exclusive events.