Final answer:
The expected number of Europeans in a conference of 150 people can be calculated by multiplying the proportion 'a' by the total number of people in the conference.
Step-by-step explanation:
In this question, we are given that the null hypothesis is that the probability of a European being selected into the club is 'a'. We are also given that the group comprises American and European political elites, with one-third and two-thirds of the group being American and European respectively.
Since the null hypothesis states that the probability of a European being selected into the club is 'a', this means that the proportion of Europeans in the group is 'a'.
If the null hypothesis is true, we can calculate the expected number of Europeans in a conference of 150 people by multiplying the proportion 'a' by the total number of people in the conference:
Expected Europeans = a * 150