Question
In: Statistics and Probability
Utilizing the data shown in the contingency table 1 below, determine whether the relationship between types...
- 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.).
-
- What are the alternative and null hypotheses (5pts)?
-
- 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
( %)
-
- 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
-
- 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
Solutions
Expert Solution
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:
| 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 |
Test statistic:
χ² = ∑ ((fo-fe)²/fe) = 0.3116
df = (r-1)(c-1) = 2
p-value = CHISQ.DIST.RT(0.3116, 2) = 0.8557
Decision:
p-value > α, Do not reject the null hypothesis.
orchestra answered 2 years agoRelated Solutions
Utilizing the data shown in the contingency table 1 below, determine whether the relationship between types...
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.).
What are the alternative and null hypotheses (5pts)?
Calculate the total column percentages (10pts.)
Gun Ownership
Types of Residential Area
Rural
Town...
Utilizing the data shown in the contingency table 1 below, determine whether the relationship between types...
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.).
Gun Ownership
Types of Residential Area
Rural
Town
City
Total
Own Gun
218
206
131
555
(
%)
No Gun
375
379...
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