Question

Exercises 1

In Australia, researchers investigated whether ``Chronic Kidney Disease" is linked to ``Hearing Loss". The participants in this study consist of a sample of 2564 adults. Kidney function was measured by a quantity called ``eGFR", which measures the kidney filtration and can be determined from a blood test. Hearing loss can be measured by an audio metric exam. Here are the results organized in a two-way table.

Hearing Loss	eGFR
	< 45	45 - 60	- 75	– 90	> 90
Yes	76	203	363	147	71
No	27	207	717	458	295

Please answer the following questions underneath each question.

1. Find the marginal distributions of “eGFR” (in percents)

(write your answers in the table below)

Answer:

eGFR	<45	45-60	60.-75	75. -90	>90
Distribution

2. Find the conditional distributions of “Hearing Loss”, given each value of “eGFR”

(write your answers in the table below)

Answer:

Hearing Loss	eGFR
	< 45	45 - 60	- 75	– 90	> 90
Yes
No

3. Are “Hearing Loss” and “Chronic Kidney Disease” associated? explain your answer

Answer:

Answer 1

	< 45	45 - 60	60-75	75-90	> 90	total
Yes	76	203	363	147	71	860
No	27	207	717	458	295	1704
total	103	410	1080	605	366	2564

1)

dividing row total with total 2564 , below is marginal distributions of “eGFR” :

< 45	45 - 60	60-75	75-90	> 90
4.02%	15.99%	42.12%	23.60%	14.27%

2)

dividing cell value with column total:

	< 45	45 - 60	60-75	75-90	> 90
Yes	0.7379	0.4951	0.3361	0.2430	0.1940
No	0.2621	0.5049	0.6639	0.7570	0.8060

(please multiply above values with 100 if required in percentage)

3)

Yes, since conditional probability for Hearing Loss is not all the same for different category in part B for a given  eGFR , this indicate that Hearing Loss” and “Chronic Kidney Disease” are associated