Question

A researcher is interested in investigating whether living situation and pet ownership are dependent. The table below shows the results of a survey. Frequencies of Living Situation and Pet Single Family Couple Dog 85 81 93 Cat 116 70 90 Various 37 51 46 None 53 53 32 What can be concluded at the a = 0.10 significance level? a. What is the correct statistical test to use? Goodness-of-Fit Independence Homogeneity Paired t-test b. What are the null and alternative hypotheses? HO: The distribution of pets is not the same for each living situation. The distribution of pets is the same for each living situation. Pet ownership and living situation are independent. Pet ownership and living situation are dependent. H: Pet ownership and living situation are dependent. The distribution of pets is the same for each living situation. Pet ownership and living situation are independent. The distribution of pets is not the same for each living situation. C. The test-statistic for this data = (Please show answer to three decimal places.) d. The p-value for this sample = (Please show your answer to four decimal places.) e. The p-value is Select an answer

Answer 1

a) Correct answer: Option (A) Goodness - of - Fit

b) Option (C) H0: Pet ownership and living situation are indepedent

Option (A) H1: Pet ownership and living situation are dependent

c) From the given data, the observed frequencies are

	Single	Family	Couple	Total
Dog	85	81	93	259
Cat	116	70	90	276
Various	37	51	46	134
None	53	53	32	138
Total	291	255	261	807

The expected frequencies are

	Single	Family	Couple	Total
Dog	93.394	81.84	83.766	259
Cat	99.5242	87.2119	89.2639	276
Various	48.32	42.342	43.338	134
None	49.762	43.606	44.632	138
Total	291	255	261	807

The chi-square contribution values are

Oi	Ei	(Oi-Ei)^2 /Ei
85	93.394	0.7544
81	81.84	0.0086
93	83.766	1.0179
116	99.5242	2.7275
70	87.2119	3.3969
90	89.2639	0.0061
37	48.32	2.652
51	42.342	1.7704
46	43.338	0.1635
53	49.762	0.2107
53	43.606	2.0237
32	44.632	3.5752
	Total:	18.3069

Degrees of freedom: 6

Test Statistic, X^2: 18.307

d) P-Value: 0.0055

e) The P-value is less than alpha 0.10

so we reject H0

Thus we conclude that Pet ownership and living situation are dependent