Question

Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 freshmen, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are given in the following table.
Strongly opposed

Freshman

Sophomore

Junior

Senior

Yes

78

72

58

36

No

22

28

42

64


To compare the four classes (freshman, sophomore, junior, senior) with respect to their opinion regarding the proposed tuition increase (yes = opposed, no = not opposed), which distribution should we calculate?

A)the joint distribution of year in school and opinion
B)the marginal distribution of year in school
C)the conditional distribution of opinion given year in school
D)the conditional distribution of year in school given opinion

Answer 1

Answer:

The option (D) the conditional distribution of year in school given opinion

Step-by-step explanation:

Solution

Given that

Results:

Group 1

Category 1 =78  (61.00)  [4.74]

Category 2 = 72  (61.00)  [1.98]

Category 3 =58  (61.00)  [0.15]

Category 4= 36  (61.00)  [10.25]  

The row totals is = 244

GROUP 2

Category 1 = 22  (39.00)  [7.41]

Category 2 = 28  (39.00)  [3.10]

Category 3 = 42  (39.00)  [0.23]

Category 4 = 64  (39.00)  [16.03]

The row totals = 156

The column totals for both group 1 and 2 in categories (1 - 4) is = 400 totals, same as the row totals.

The distribution to calculate is, the conditional distribution of year in school given opinion