Question

Using α = 0.01, test that there was no relationship between survival and age category. Refer to the output in part (a). 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.

Output from part A

Contingency table results:

Rows: Survival
Columns: Bin(Age)

Cell format

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

	1 to 7	7 to 13	13 to 19	19 to 25	25 to 31	31 to 37	37 to 43	43 to 49	49 to 55	55 to 61	61 to 67	Total
Died	12 (30%) (57.14%) (13.79%)	2 (5%) (15.38%) (2.3%)	1 (2.5%) (8.33%) (1.15%)	2 (5%) (28.57%) (2.3%)	12 (30%) (70.59%) (13.79%)	4 (10%) (57.14%) (4.6%)	0 (0%) (0%) (0%)	3 (7.5%) (75%) (3.45%)	0 (0%) (0%) (0%)	3 (7.5%) (100%) (3.45%)	1 (2.5%) (100%) (1.15%)	40 (100%) (45.98%) (45.98%)
Survived	9 (19.15%) (42.86%) (10.34%)	11 (23.4%) (84.62%) (12.64%)	11 (23.4%) (91.67%) (12.64%)	5 (10.64%) (71.43%) (5.75%)	5 (10.64%) (29.41%) (5.75%)	3 (6.38%) (42.86%) (3.45%)	1 (2.13%) (100%) (1.15%)	1 (2.13%) (25%) (1.15%)	1 (2.13%) (100%) (1.15%)	0 (0%) (0%) (0%)	0 (0%) (0%) (0%)	47 (100%) (54.02%) (54.02%)
Total	21 (24.14%) (100%) (24.14%)	13 (14.94%) (100%) (14.94%)	12 (13.79%) (100%) (13.79%)	7 (8.05%) (100%) (8.05%)	17 (19.54%) (100%) (19.54%)	7 (8.05%) (100%) (8.05%)	1 (1.15%) (100%) (1.15%)	4 (4.6%) (100%) (4.6%)	1 (1.15%) (100%) (1.15%)	3 (3.45%) (100%) (3.45%)	1 (1.15%) (100%) (1.15%)	87 (100%) (100%) (100%)

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	10	25.908103	0.0039

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

Answer 1

In this question we are testing the chi square test for independence. We need to check if there is relationship between survial and age category.

Hypothesis

Ho: There is no relationship between survival and age category.

H1 : There is a relationship between survival and age category

From the output of the chi square test of independence we check the pvalue. The pvalue is 0.0039 which is less than 0.01(level of signficance). Hence we reject the null hypothesis and conclude that there is a relationship between survival and age category