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A bank categorizes its customers into one of three groups based on their banking habits. A random sample of 30 customers from each group was selected, and the number of times each customer visited the bank during the past year was recorded. The following table shows the summary statistics.
The bank manager will investigate whether there is a significant difference in mean numbers of bank visits for the groups. Multiple two-sample t-tests will be conducted, each at the significance level of α=0.05.
(a) How many t-tests will need to be conducted for the manager’s investigation? List the pairs of groups for each test.
The family error rate is the
(b) 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.
(c) 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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