Question

8.2.11 Many studies have been done to look at the relationship between heart disease and baldness. In one study, researchers selected a sample of Stot1 heart disease male patients and a control group of Stot2 male patients not suffering from heart disease from hospitals in eastern Massachusetts and Rhode Island. Each was asked to classify their degree of baldness. The results are given in the following table. Use these data to answer the following questions. Baldness None Little Some Much Total Yes 270 154 221 40 685 Heart disease No 381 263 220 33 897 Total 651 417 441 73 1582 Identify the observational units. People suffering from heart disease Describe the parameter(s) of interest and assign appropriate symbol(s) to the parameter(s). State in words the appropriate null and alternative hypotheses in the context of the study. State in symbols the appropriate null and alternative hypotheses in the context of the study. Null: Tone Little Tsome * TTMuch Alt: TTNone= TLittle = TTSome = TTMuch O Null: At least one population proportion is different from the others. Alt: TTNone TTLittle TT Some = TIMuch- O Null: Tong = TTLittle Tsome = TTMuch Alt: At least one population proportion is different from the others. O Null: TTNon = TTLittle Tsome TTMuch Alt: None TTLittle TSama TMuch

these are the options for the above questions

Answer 1

using excel>addin>phstat>multiple sample test >chi square

we have

Chi-Square Test
Observed Frequencies
	Baldness						Calculations
Heart Diseases	None	Little	Some	Much	Total		fo-fe
Yes	270	154	221	40	685		-11.8805	-26.5594	30.04867	8.391277
No	381	263	220	33	897		11.88053	26.55942	-30.0487	-8.39128
Total	651	417	441	73	1582
Expected Frequencies
	Baldness
Heart Diseases	None	Little	Some	Much	Total		(fo-fe)^2/fe
Yes	281.8805	180.5594	190.9513	31.60872	685		0.500733	3.906762	4.728549	2.227661
No	369.1195	236.4406	250.0487	41.39128	897		0.382388	2.983425	3.610988	1.701168
Total	651	417	441	73	1582
Data
Level of Significance	0.05
Number of Rows	2
Number of Columns	4
Degrees of Freedom	3
Results
Critical Value	7.814728
Chi-Square Test Statistic	20.04168
p-Value	0.000166
Reject the null hypothesis

observational unit: people suffering from heart diseases

the population proportion of man with heart diseases in each baldness group( $\pi$ )

Null : there is no association between baldness and heart diseases

Alt:there is an association between baldness and heart diseases .

the null and alternative hypothesis is given by option C

Chi square = 20.042

P value = 0.0002

Since p value is less than 0.05 so reject Ho . and conclude that there is an association between baldness and heart diseases ..

Scope : option B is true