Question

1. A company that makes pet food is interested in creating dry and canned pet food. The company is also interested in what cats and dogs prefer their pet food to be (dry or canned). At the 5% significance level can you conclude that type of pet is independent of pet food choice?

   	Canned	Dry	Total
   Dog	25	25	50
   Cat	20	30	50
   Total	45	55	100

   		Reject the null hypothesis, type of pet is independent of pet food choice
   		Reject the null hypothesis, whether the pet prefers canned or dry is dependent upon whether the pet is a cat or a dog
   		Do not reject the null hypothesis, type of pet is independent of pet food choice
   		Do not reject the null hypothesis, whether the pet prefers canned or dry is dependent upon whether the pet is a cat or a dog

Answer 1

H0:  Type of pet is independent of pet food choice

H1:  Type of pet is not independent of pet food choice

The observed frequencies are

Gender	Canned	Dry	Total
Dog	25	50	75
Cat	30	50	80
Total	55	100	155

.

The Expected frequencies are

Gender	Canned	Dry	Total
Dog	26.613	48.387	75
Cat	28.387	51.613	80
Total	55	100	155

The Chi-square contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
25	26.613	0.0978
50	48.387	0.0538
30	28.387	0.0917
50	51.613	0.0504
	Total:	0.2937

Degrees of freedom: 1

Test Statistic, X^2: 0.2937

Critical X^2: 3.841456

P-Value: 0.5879

since Chi-square value 0.2937 > Chi-squaer critical value 3.841456 so we accept H0

and also P-value > alpha 0.05 so we accept H0

Thus we conclude that Type of pet is independent of pet food choice

Correct answer: Option (C) Do not reject the null hypothesis, type of pet is independent of pet food choice