Question

Pregnant sows are usually placed in a farrowing crate a few days prior to giving birth and remain confined for several weeks afterward. Because of the close confinement, it is not unusual for the sow to develop skin ulcers (“bedsores”) from laying on the floor of the crate. An animal scientist conducted an experiment to compare two types of crate flooring (plastic coated expanded metal flooring or a concrete slab serving as the floor) for their effect on the development of skin ulcers.

Pregnant sows were randomly assigned to a floor type and observed for skin ulcers throughout the confinement period. Of the 45 sows assigned to the crates with plastic coated expand metal floors, 29 developed skin ulcers. In contrast, only 23 of the 48 sows assigned to crates with concrete floors developed skin ulcers.

1. Test an appropriate set of hypotheses to determine if there is a difference in the percentage of sows developing skin ulcers based on the floor type of the crate. Use " = 0.05. State your conclusion in the context of the problem.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

p1cap = X1/N1 = 29/45 = 0.6444
p1cap = X2/N2 = 23/48 = 0.4792
pcap = (X1 + X2)/(N1 + N2) = (29+23)/(45+48) = 0.5591

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.6444-0.4792)/sqrt(0.5591*(1-0.5591)*(1/45 + 1/48))
z = 1.60

P-value Approach
P-value = 0.1096
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that there is a difference in the percentage of sows developing skin ulcers based on the floor type of the crate