Question 2 (28 points):

In a research on the entrepreneurial potential and business start-up intentions of CEGEP students and graduates, the following cross-tabulation of the distribution of entrepreneurial potential (obtained with the help of an assessment test) according to the parents' sector of work is obtained. The theoretical distribution of respondents is also given, based on the hypothesis that the two characteristics are independent.

Theoretical distribution

Entrepreneurial potential

Low

Moven

High

31.5163

223.2042

77.2796

23.3524

57.2614

18.1313

73.0

128.4096

517.0

179.0

a) Find the value of the theoretical frequencies for

1) the box (2,2), combination of the modalities Private-Average.

ii) box (3,3), combination of the terms On their own account-Strong

b) Are the conditions for the test of independence of two characteristics satisfied? Explain.

c) We want to determine the disparity between the observed distribution and the theoretical distribution of absolute frequencies under the hypothesis of independence.

Complete the following table.