A random sample of 250 patients was selected and their workout timing

Question

A random sample of 250 patients was selected and their workout timing and diabetes status were recorded. The following table shows the workout timing and severity of diabetes:

Workout (in minutes)	Severity of diabetes status
	Low	Moderate	High
0 −15	06	27	19
15 to 30	08	36	17
30 to 45	21	45	33
≥ 45	14	18	06

Test at 5% level of significance whether workout habit and diabetes are associated with to each other or not.

20 Feb 2025

Answer :

Word Count : 277

To test whether workout habits and diabetes severity are associated, we perform a Chi-square test for independence. Here are the steps: ### Step 1: Define Hypotheses - Null Hypothesis \(H_0\): Workout habits and diabetes severity are independent (no association). - Alternative Hypothesis \(H_a\): Workout habits and diabetes severity are dependent (associated). ### Step 2: Organize the Observed Data The table provides the observed frequencies: | Workout Time (minutes) | ____ ____ ____ ________ ____ ____ ______.
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Disease	Test result		Total
	+	–
Present	170	30	200
Absent	20	280	300

	Lung Cancer	No Lung Cancer	Total
Smokers	100	1220	1320
Non-smokers	50	2260	2310

S. No.	Serum Cholesterol (mg/dl)	Weight (kg)	Number of Patients having CHD	Total Number of Patients
1	420	60	10	20
2	450	68	15	30
3	400	54	4	15
4	510	74	2	10
5	480	62	1	5

Risk Factor	Parameter Estimate	SE
Age	0.150	0.010
Gender	0.450	0.150
Systolic Blood Pressure	0.015	0.008
Smoking	0.650	0.170
Total Serum Cholesterol	0.002	0.004
Diabetes	-0.350	0.250