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.