Question

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-scientific), and "Degree" with 3 categories (Ju- nior, Bachelor and Graduate). The numbers in the table are the counts of adults in each level of Opinion by each level of Degree, however, there are some missing counts Table 1 Degree Opinion Junior Bachelor | Graduate Total Not scientific 122 268 Very or sort of scientific 106 31 13 1. If "Opinion" and "Degree" are independent, what are the values of the missing counts? (explain your answer) 2. Find the marginal distribution of Degree Actually, the Two-way table of observed counts is the following. Table 2: Degree Opinion Junior Bachelor| Graduate Not scientific 122 44 102 Very or sort of 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

1.

	Junior	Bachelor	Graduate	Row Total
Not scientific	78	122	68	268
scientific	31	62	13	106
Column Total	109	184	81	374

If Opinion and degree are independent then

cell = (Row total)*(column total)/Total

that is , 31 = (106)*(column total)/ 374

therefore column total = 109 (rounding)

2. Marginal distribution of degree

Degree	Probability
Junior	109/374= 0.29
Bachelor	184/374=0.49
Graduate	81/374=0.22

3.

	Junior	Bachelor	Graduate	Row Total
Not scientific	44	122	102	268
scientific	31	62	13	106
Column Total	75	184	115	374

Marginal distribution of Opinion

Opinion	Probability
Not scientific	268/374=0.72
Scientific	106/374=0.28

4.

	Junior	Bachelor	Graduate
Not Scientific	44/75=0.59	122/184=0.66	102/115=0.89
Scientific	31/75=0.41	62/184=0.34	13/115= 0.11

Note : P(Not scientific I Junior ) = P(Not scientific $\bigcap$ Junior)/ P(Junior)= (44/374)/(75/374) = 0.59

5.We got that

P(Not scientific I Junior )= 0.59

P(Not scientific) = 0.72

Thus ,

P(Not scientific I Junior ) $\neq$ P(Not scientific)

We can say that Opinion is not independent of Degree

We can conclude that , Opinion is associated with degree