Question

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Table 1 presents data on the opinion of a group of adults about astrology. There are two variables; "Opinion" with 2 categories (Not-scientific and Sort-of-scient ific), and "Degree" with 3 categories (Ju- nior, Bachelor and Graduate). The numbers in the table are the counts of adults each level of Opinion by each level of Degree, however, there are some missing counts. Table 1: Degree Opinion Junior Bachelor Graduate Tot al Not scientific 122 268 Very or sort of scientific 31 13 106 1. If "Opinion" and "Degree" are independent, what are the values of the missing counts? (explain your answer). 2. Find the marginal distribution of Degre Actually, the Two-way table of observed counts the following Table 2: Degree Opinion Junior Bachelor Graduate Not scientific 44 122 102 Very or sort f scientific 31 62 13 3. Find the marginal distributions of Opinion 4. Find the conditional distributions of Opinion, given each value of Degree. (write your answer in a table). 5. Is Opinion associated to Degree? (explain your answer). What do you conclude?

Answer 1

Soluction from dhe gun data iedependent dugese Opinien ard are Junioor Bachelar Graduate Row Total 268 Scieatific 78 68 192 Not scientific 31 62 106 13 184 3p4 LColunn total t09 Opinion anol (Rous total) x CColoumn tslal)/Total thus, 31- Clo6) Ccolemn total)/314 Thus, tolumn total (Junion) 109 ( 9taunded) Tbop independent Coll- got loy add ing and subtracting Othem Values ute Marginal Potebility datibudticodlegra Probalaility 109/34 Degres 0.2914 Junion 184/314 O.4920 Bachelan 81/3t4 O.2166 Gracluate

3 Margel disbi butions t opinien Junior Bachelar lGduate Rous Tota (22 268 Not Scientific 니니 l02 62 31 Scientific (3 (D6 184 1tS Column total 374 Marginal oitn bution Opmien Probaloility OPinion 268/3+4 Not Scientifc 991 0 O.2834 Scientific t06/3-14- distibutions pinion ) Conolitional Graduate Bachelos Tunion 122/184-04630 uu 0.5867 22/18 at88.0 S/GO Not Saentihe 5 0니133| 62/184-0. 3370D-130 13/15>0-130 2 scientihic Note PCMot Scientific 1juniar)- PC S and Cuu/374)/75/374)-0-5867 junian) PCunor ) =

Opinion as0iateol to Degree 5 pCnot Scentihic Junior 0.5967 P Crot Scient.fc) -0.7166 : PINOE dceutifc juniort PCnot Scerthe) ad Opinton is not independat ule Can of Dagre conclude that opnion and degree asoiatedl e