Question

Using α = 0.01, test that there was no relationship between survival and group size. State the null and alternative hypotheses. Report the value of the appropriate test statistic, the distribution of the test statistic under the null hypothesis, and the P-value of the test to answer the question. State your conclusion.

Data:

Contingency table results:

Rows: Group Size
Columns: Survival

Cell format

Count
(Row percent)
(Column percent)
(Percent of total)

	Died	Survived	Total
1	13 (81.25%) (32.5%) (14.94%)	3 (18.75%) (6.38%) (3.45%)	16 (100%) (18.39%) (18.39%)
2	2 (50%) (5%) (2.3%)	2 (50%) (4.26%) (2.3%)	4 (100%) (4.6%) (4.6%)
3	1 (33.33%) (2.5%) (1.15%)	2 (66.67%) (4.26%) (2.3%)	3 (100%) (3.45%) (3.45%)
4	5 (62.5%) (12.5%) (5.75%)	3 (37.5%) (6.38%) (3.45%)	8 (100%) (9.2%) (9.2%)
7	0 (0%) (0%) (0%)	6 (100%) (12.77%) (6.9%)	6 (100%) (6.9%) (6.9%)
9	0 (0%) (0%) (0%)	9 (100%) (19.15%) (10.34%)	9 (100%) (10.34%) (10.34%)
12	5 (41.67%) (12.5%) (5.75%)	7 (58.33%) (14.89%) (8.05%)	12 (100%) (13.79%) (13.79%)
13	6 (46.15%) (15%) (6.9%)	7 (53.85%) (14.89%) (8.05%)	13 (100%) (14.94%) (14.94%)
16	8 (50%) (20%) (9.2%)	8 (50%) (17.02%) (9.2%)	16 (100%) (18.39%) (18.39%)
Total	40 (45.98%) (100%) (45.98%)	47 (54.02%) (100%) (54.02%)	87 (100%) (100%) (100%)

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	8	22.073269	0.0048

Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.

Answer 1

Result:

Using α = 0.01, test that there was no relationship between survival and group size. State the null and alternative hypotheses. Report the value of the appropriate test statistic, the distribution of the test statistic under the null hypothesis, and the P-value of the test to answer the question. State your conclusion.

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	8	22.073269	0.0048

Chi square test is used to test the association between survival and group size.

Ho: there is no association between survival and group size

H1: there is an association between survival and group size

Computed chi square =22.0733, DF= 8, P=0.0048. The p value 0.0048 which is < 0.05 , the level of significance. Ho is rejected.

There is enough evidence to conclude that there is significant association between survival and group size.