Question

An apartment complex surveyed its tenants and asked a variety of questions about their living arrangements. One question asked for the renter’s marital status using categorical responses of single, married, divorced, and widowed. Another question asked for the renter’s pet ownership with the categorical Dog, Cat, both (cat and dog) and none (neither cat nor dog).

1. Methods: Explicitly state and conduct the appropriate hypothesis test to determine if there is any relationship between pet ownership and marital status? (All steps should be included)
2. Discussion: Interpret the statistical decision you arrived at in terms that would be useful for apartment policies and procedures. This section should also include suggestions for further research and/or discussion of additional variables that may provide more precise results.

   Marital Status	Pets
   Divorced	none
   Widowed	both
   Single	cat
   Divorced	dog
   Single	Dog
   Married	cat
   Single	both
   Married	cat
   Single	cat
   Widowed	none
   Divorced	cat
   Married	Dog
   Single	none
   Married	none
   Divorced	Dog
   Married	cat
   Widowed	both
   Married	none
   Married	none
   Widowed	cat
   Divorced	both
   Single	cat
   Single	Dog
   Single	Dog
   Married	none
   Married	Dog
   Single	Dog
   Married	cat
   Single	cat
   Single	both
   Married	cat
   Divorced	Dog
   Divorced	none
   Married	both
   Married	both
   Widowed	dog
   Married	both
   Married	cat
   Single	cat
   Widowed	none
   Divorced	cat
   Married	Dog
   Divorced	both
   Single	cat
   Single	Dog

Answer 1

An apartment complex surveyed its tenants and asked a variety of questions about their living arrangements. One question asked for the renter’s marital status using categorical responses of single, married, divorced, and widowed. Another question asked for the renter’s pet ownership with the categorical Dog, Cat, both (cat and dog) and none (neither cat nor dog).

1. Methods: Explicitly state and conduct the appropriate hypothesis test to determine if there is any relationship between pet ownership and marital status? (All steps should be included)

Two-Way Table
Count of Marital Status	Pets
Marital Status	both	cat	dog	none	Grand Total
Divorced	2	2	3	2	9
Married	3	6	3	4	16
Single	2	6	5	1	14
Widowed	2	1	1	2	6
Grand Total	9	15	12	9	45

H0: There is no relationship between pet ownership and marital status

H0: There is a relationship between pet ownership and marital status

Chi-Square Test
Observed Frequencies
	Column variable						Calculations
Row variable	both	cat	dog	none	Total		fo-fe
Divorced	2	2	3	2	9		0.2000	-1.0000	0.6000	0.2000
Married	3	6	3	4	16		-0.2000	0.6667	-1.2667	0.8000
Single	2	6	5	1	14		-0.8000	1.3333	1.2667	-1.8000
Widowed	2	1	1	2	6		0.8000	-1.0000	-0.6000	0.8000
Total	9	15	12	9	45
Expected Frequencies
	Column variable
Row variable	both	cat	dog	none	Total		(fo-fe)^2/fe
Divorced	1.8000	3.0000	2.4000	1.8000	9		0.0222	0.3333	0.1500	0.0222
Married	3.2000	5.3333	4.2667	3.2000	16		0.0125	0.0833	0.3760	0.2000
Single	2.8000	4.6667	3.7333	2.8000	14		0.2286	0.3810	0.4298	1.1571
Widowed	1.2000	2.0000	1.6000	1.2000	6		0.5333	0.5000	0.2250	0.5333
Total	9	15	12	9	45
Data
Level of Significance	0.05
Number of Rows	4
Number of Columns	4
Degrees of Freedom	9
Results
Critical Value	16.9190
Chi-Square Test Statistic	5.1877
p-Value	0.8176
Do not reject the null hypothesis

Calculated chi square = 5.1877 < critical chi square 16.919 at 0.05 level of significance.

Ho is not rejected.

We conclude that there is no relationship between pet ownership and marital status.

2. Discussion: Interpret the statistical decision you arrived at in terms that would be useful for apartment policies and procedures. This section should also include suggestions for further research and/or discussion of additional variables that may provide more precise results.

We conclude that there is no relationship between pet ownership and marital status. It may be useful for apartment policies. Additional variables that may provide more results are gender and ethnicity.