Question

1. Chi-square test.

On your fish farm, you have been growing tilapia in four ponds. Each pond gets a different feed (a, b, c, and d). After a few months you harvest the fish in each pond and get a total weight. The data are given below. Use a Chi-Square test to see if there is a difference between feeds, use α = 0.05, write the H0, give the P-value, and write a conclusion.

feed           pounds of fish produced

a                            39

b                            44

c                            50

d                            41

Answer 1

Category	Observed Frequency (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
a	39	0.25	174 * 0.25 = 43.5	(39 - 43.5)²/43.5 = 0.4655
b	44	0.25	174 * 0.25 = 43.5	(44 - 43.5)²/43.5 = 0.0057
c	50	0.25	174 * 0.25 = 43.5	(50 - 43.5)²/43.5 = 0.9713
d	41	0.25	174 * 0.25 = 43.5	(41 - 43.5)²/43.5 = 0.1437
Total	174	1.00	174	1.5862

Null and Alternative hypothesis:  
Ho: Proportions are same.  
H1: Proportions are different.  
Test statistic:  
χ² = ∑ ((O-E)²/E) = 1.5862
df = n-1 =    3
p-value = CHISQ.DIST.RT(1.5862, 3) = 0.6625  
Decision:  
p-value > α, Do not reject the null hypothesis  
There is not enough evidence to conclude that there is a difference between feeds at 0.05 significance level.