Question

With a random sample of fifty-seven rats captured in a center, twelve are b-breed, nineteen are y-breed, and twenty-six are w-breed. Do you find there is significant evidence that b-breed, y-breed, and w-breed rats do not seem to be equally represented in the center's rat population?

Test the null hypothesis as to if there is equal representation of the three rat breeds at significance level 5%. Show the null and alternative hypotheses, your significance level, the chi-square value you calculate, the pvalue calculated with your chi square table, and make a statement comparing the pvalue with the significance level.

Answer 1

Null hypothesis :there is equal representation of the three rat breeds

Alternative hypothesis :there is not equal representation of the three rat breeds

significance level = 0.05

the chi-square value :

o	E	O-E	(O -E)^2	(O -E)^2/ E
12	19	-7	49	2.57894737
19	19	0	0	0
26	19	7	49	2.57894737
57	57		98	5.15789474

chi-square value = 5.158

P value :

with chi-square value = 5.158 , df = 2

we get p value =  .07585

Conclusion :

p value > l.o.s

0.07585 > 0.05

so fail to reject null hypothesis

At alpha = 0.05 l.o.s there is enough evidence to claim that  there is equal representation of the three rat breeds