Question

1. Utilizing the data shown in the contingency table 1 below, determine whether the relationship between types of residential area and gun ownership is statistically significant. Once you have arrived at an answer for each question, please write a sentence or two interpreting the results, you may want to round the decimals to the nearest whole number (70 pts.).

1. 1. What are the alternative and null hypotheses (5pts)?
2. 2. Calculate the total column percentages (10pts.)

Gun Ownership	Types of Residential Area
	Rural	Town	City	Total
Own Gun	218	206	131	555 (         %)
No Gun	375	379	235	989 (           %)
Total	593	585	366	1544 (           %)

3. Calculate the expected frequency for each cell and explain the meaning of expected frequencies (15 pts).

Gun Ownership	Types of Residential Area
	Rural	Town	City	Total
Own Gun				555
No Gun				989
Total	593	585	366	1544

4. Calculate chi-square (χ ²) for each cell using to the formula (Oi − Ei )²/ Ei (15pt).

Gun Ownership	Types of Residential Area
	Rural	Town	City	Total
Own Gun
No Gun
Total

5. What is the Chi-square statistic(5 pt)? And what is the critical value for this case at 5% significance level, what information did you use to find it (10pts)?

6. Draw a conclusion about your null hypothesis at 5% significance level, and explain how did you arrive that conclusion (10pt).

Answer 1

a) Null and alternative hypothesis:

Ho: Types of residential area and gun ownership are independent.

Ha: Types of residential area and gun ownership are dependent.

b) Percentage:

555/1544 *100 = 35.95%

989/1544 *100 = 64.05%

1544/1544*100 = 100%

c) Expected frequencies:

	Rural	Town	City	Total
Own Gun	593 * 555 / 1544 = 213.1574	585 * 555 / 1544 = 210.2817	366 * 555 / 1544 = 131.5609	555
No Gun	593 * 989 / 1544 = 379.8426	585 * 989 / 1544 = 374.7183	366 * 989 / 1544 = 234.4391	989
Total	593	585	366	1544

d)

	(fo-fe)²/fe
Own Gun	(218 - 213.1574)²/213.1574 = 0.11	(206 - 210.2817)²/210.2817 = 0.0872	(131-131.5609)²/131.5609 = 0.0024
No Gun	(375-379.8426)²/379.8426 = 0.0617	(379-374.7183)²/374.7183 = 0.0489	(235-234.4391)²/234.4391 = 0.0013

e)

Chi-square test statistic:  

χ² = ∑ ((fo-fe)²/fe) = 0.3116

df = (r-1)(c-1) = 2

Critical value:

χ²α = CHISQ.INV.RT(0.05, 2) = 5.9915

f)

Decision:  

As χ² = 0.3116 < χ²α, Do not reject the null hypothesis. There is not enough evidence to conclude that there is a significant relationship between types of residential area and gun ownership