Question 15.36

15.36 Trust of individuals and groups.

Trust is an essential element in any exchange of goods or services. The following trust game is often used to study trust experimentally:

A sender starts with $X and can transfer any amount to a responder. The responder then gets and can transfer any amount back to the sender. The game ends with final amounts and for the sender and responder, respectively.

The value x is taken as a measure of the sender’s trust, and the value indicates the responder’s trustworthiness. A study used this game to study the dynamics between individuals and groups of three.14 The following table summarizes the average amount x sent by senders.

Sender Responder
Individual Individual 32 65.5 36.4
Individual Group 25 76.3 31.2
Group Individual 25 54.0 41.6
Group Group 27 43.7 42.4
  1. Find the pooled estimate of the standard deviation for this study and its degrees of freedom.
  2. Is it reasonable to use a pooled standard deviation for the analysis? Explain your answer.
  3. Compute the marginal means.
  4. Plot the means. Do you think there is an interaction? If yes, then describe it.
  5. The statistics for sender, responder, and interaction are 9.05, 0.001, and 2.08 respectively. Compute the -values and state your conclusions.