Psychologists conducted an experiment to investigate the effect of anxiety on a person's desire to be alone or in the company of others. A group of 30 individuals were randomly assigned into two groups; one group was designated the "high anxiety" group and the other the "low anxiety" group. Those in the high-anxiety group were told that in the "upcoming experiment", they would be subjected to painful electric shocks, while those in the low-anxiety group were told that the shocks would be mild and painless. All individuals were informed that there would be a 10 minute wait before the experiment began, and that they could choose whether to wait alone or with other participants.

The following table summarizes the results:

(a) Under the null hypothesis of no association, what are the expected cell counts?

(b) Under the assumption that the marginal totals are fixed and the null hypothesis is true, what is the probability of the observed set of results?

(c) Enumerate the tables that are more extreme than what was observed, in the same direction.

(d) Conduct a formal test of association for the results and summarize your findings. Let \(\alpha=0.05\).

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Wait Together Wait Alone Sum High-Anxiety Low-Anxiety 12 5 17 4 9 13 Sum 16 14 30