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.

i) 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"

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

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

Answer 1

	XL	L	S
Not organic feed	25	125	30
Organic feed	50	50	20

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

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

Answer: "P(is not fed organic feed)" and "P(lays extra large eggs)" are dependent.

Explanation:

From table, the intersection of 'lays XL eggs' and 'not organic feed' = 25

P(lays extra-large eggs and is not fed organic feed) = 25 / 300 = 0.8333

P(is not fed organic feed) *P(lays extra large eggs) = 0.60*0.25 = 0.15

Since, P(lays extra-large eggs and is not fed organic feed) is not equal to P(is not fed organic feed) *P(lays extra large eggs) , we can say that "P(is not fed organic feed)" and "P(lays extra large eggs)" are dependent.

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

Answer: "is organic fed" and "is not organic fed" are mutually exlusive events.

Explanation:

From Table, there is no intersection value of "is organic fed" and "is not organic fed". Which means no chicken can be both not fed organic feed and fed organic feed.

P("is organic fed" and "is not organic fed") = 0.

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

Answer: "lays large eggs" and "lays small eggs" are mutually exclusive events

Explanation:

As in previous case, both lays small eggs and lays large eggs do not happen together.

P("lays large eggs" and "lays small eggs") = 0.(from above table).

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

The relative risk for the trait "lays extra-large eggs" with risk factor "is fed organic feed" is 3.00

Explanation:

Relative risk (RR) for the trait "lays extra-large eggs" with risk factor "is organic feed" is gievn by:

RR = P("lays extra large eggs " given "is organic fed") / P("lays extra large eggs " given "is not organic fed")

P("lays extra large eggs " given "is organic fed") = 50/120 = 5/12

P("lays extra large eggs " given "is not organic fed") = 25/180 = 5/36

RR = (5/12) /(5/36) = 3