In a recent health survey, 1300 randomly selected US adult citizens were asked a

Question

In a recent health survey, 1300 randomly selected US adult citizens were asked a series of questions regarding their health and their financial status. The answers provided by the respondents allow the investigators to categorize each one into a health level and a socioeconomic class. A contingency table summarizing the results of this survey is provided below.
Assume that this is a representative sample of US adults and that the answers provided were truthful.

A) In this study the Health Assessment variable is:

---Select---

Qualitative & Nominal

Qualitative & Ordinal

Quantitative & Discrete

Quantitative & Continuous

Qualitative & Discrete

Qualitative & Continuous

Quantitative & Nominal

Quantitative & Ordinal

Consider that you randomly select one of these records from the 1300 responses; use the results published in Table 1, above, to find the following probabilities
Note: You may answer in fraction (n/d) form. If you compute a decimal answer, use at least 5-decimal precision

B) P(Poor Health) =  
C) P(Upper Class) =  
D) P(Poor Health|Low Class) =  
E) P(Poor Health|Upper Class) =  
F) P(Working Class & Excellent Health) =  
G) P(Good or Excellent Health) =  
H) P(Fair Health Working Class) =  
I) P([Excellent Health]c) =  
J) P(Middle Class | Good Health) =  
K) P([Middle Class]c | Good Health) =  
L) P(Middle Class | [Good Health]c) =  

M) From the choices below, which of the events are mutually exclusive?
     Note choices are in the form 'Social Class / Health Assessment'

Low/Poor

Working/Poor

Low/Good

Middle/Fair

Middle/Poor

Upper/Excellent

Low/Excellent

Middle/Excellent

Middle/Good

Upper/Poor

Working/Fair

Upper/Good

Upper/Fair

Working/Excellent

Working/Good

Low/Fair

Health Assessment Social Class Poor Fair Good Excellent Low 9 14 17 0 Working 94 83 155 172 Middle 47 40 85 398 Upper 6 6 81 93

Explanation / Answer

a)

In this study the Health Assessment variable is: Qualitative & Ordinal

from above:

B)

P(Poor Health) = 156/1300 =3/25

c) P(Upper Class) = =186/1300=93/650

d) P(Poor Health|Low Class) = 9/40

e)P(Poor Health|Upper Class) = 6/186 =1/31

f) P(Working Class & Excellent Health) = 172/1300 =43/325

g)P(Good or Excellent Health) = (338+663)/1300=1001/1300 =77/100

h)P(Fair Health Working Class) = (172+143-83)/1300=232/1300 =58/325

i)I) P([Excellent Health]c) = 1-663/1300=637/1300

j) J) P(Middle Class | Good Health) = 85/338

k) K) P([Middle Class]c | Good Health) = (1-85/338) =253/338

l) L) P(Middle Class | [Good Health]c) = (570-85)/(1300-338)=485/962

M)

mutually exclusive:

Low/Excellent

Health Assessment Social Class Poor Fair Good Excellent total Low 9 14 17 0 40 Working 94 83 155 172 504 Middle 47 40 85 398 570 Upper 6 6 81 93 186 total 156 143 338 663 1300

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