The bank manager knows that the investigation will involve conducting multiple two-sample  t-tests. The manager begins the investigation by considering two different  t-tests as independent, successive trials. The possible outcomes of the trials,  N or  S, are shown in the following tree diagram.

(ii) The family error rate is the probability of obtaining a significant result for  at least one of the  t-tests conducted, under the assumption that the null hypothesis is true. Use the tree diagram to determine the family error rate for two  t-tests, each conducted at a level of  α=0.05. Show your work.

(c) Determine the family error rate for the number of  t-tests identified in part (a), each conducted at a level of  α=0.05. Show your work.

The manager wants the family error rate to be close to 0.05. Suggest a single significance level  α that could be used for all of the individual  t-tests that will bring the family error rate close to  0.05. Show work to support your suggested level.

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